Space of modular forms of level 6930, weight 2, and trivial character

• Label: 6930.2.a
• Level: $6930$
• Weight: $2$
• Character orbit: 6930.a
• Rep. character: $\chi_{6930}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $65$
• Sturm bound: $3456$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6930.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 65 \)
Sturm bound:			\(3456\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(13\), \(17\), \(19\), \(23\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6930))\).

	Total	New	Old
Modular forms	1760	100	1660
Cusp forms	1697	100	1597
Eisenstein series	63	0	63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(5\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
Plus space					\(+\)	\(42\)
Minus space					\(-\)	\(58\)

Trace form

\( 100 q + 100 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6930))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs					Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	7	11
6930.2.a.a	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.b	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.c	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.d	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.e	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.f	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.g	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.h	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.i	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.j	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.k	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.l	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.m	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.n	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.o	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.p	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.q	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.r	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.s	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.t	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.u	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.v	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.w	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.x	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.y	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.z	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ba	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bb	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bc	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bd	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.be	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bf	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bg	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bh	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bi	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bj	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bk	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bl	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bm	$6930$	$2$	6930.a	1.a	$1$	$1$	$1$	$55.336$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bn	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bo	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bp	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bq	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.br	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bs	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bt	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bu	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bv	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bw	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bx	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.by	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bz	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ca	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.cb	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.cc	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cd	$6930$	$2$	6930.a	1.a	$1$	$2$	$2$	$55.336$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.ce	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	3.3.316.1	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-3\)	\(-3\)		$+$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.cf	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	3.3.316.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.cg	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.ch	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	3.3.148.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$+$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.ci	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(3\)	\(3\)		$+$	$+$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.cj	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ck	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(3\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cl	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	3.3.892.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cm	$6930$	$2$	6930.a	1.a	$1$	$3$	$3$	$55.336$	3.3.316.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6930))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6930)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3465))\)\(^{\oplus 2}\)