Space of modular forms of level 6034, weight 2, and trivial character

• Label: 6034.2.a
• Level: $6034$
• Weight: $2$
• Character orbit: 6034.a
• Rep. character: $\chi_{6034}(1,\cdot)$
• Character field: $\Q$
• Dimension: $215$
• Newform subspaces: $18$
• Sturm bound: $1728$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1728\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6034))\).

	Total	New	Old
Modular forms	868	215	653
Cusp forms	861	215	646
Eisenstein series	7	0	7

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

\(2\)	\(7\)	\(431\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(28\)
\(+\)	\(+\)	\(-\)	$-$	\(25\)
\(+\)	\(-\)	\(+\)	$-$	\(27\)
\(+\)	\(-\)	\(-\)	$+$	\(26\)
\(-\)	\(+\)	\(+\)	$-$	\(32\)
\(-\)	\(+\)	\(-\)	$+$	\(23\)
\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(-\)	\(-\)	$-$	\(33\)
Plus space			\(+\)	\(98\)
Minus space			\(-\)	\(117\)

Trace form

\( 215 q + 3 q^{2} + 8 q^{3} + 215 q^{4} + 6 q^{5} - q^{7} + 3 q^{8} + 219 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\) 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	7	431
6034.2.a.a	$6034$	$2$	6034.a	1.a	$1$	$1$	$1$	$48.182$	\(\Q\)	None	✓	$1$	$2$	\(-1\)	\(-3\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{7}+\cdots\)
6034.2.a.b	$6034$	$2$	6034.a	1.a	$1$	$1$	$1$	$48.182$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}+q^{7}+\cdots\)
6034.2.a.c	$6034$	$2$	6034.a	1.a	$1$	$1$	$1$	$48.182$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-q^{7}+\cdots\)
6034.2.a.d	$6034$	$2$	6034.a	1.a	$1$	$1$	$1$	$48.182$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
6034.2.a.e	$6034$	$2$	6034.a	1.a	$1$	$1$	$1$	$48.182$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
6034.2.a.f	$6034$	$2$	6034.a	1.a	$1$	$1$	$1$	$48.182$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(3\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}-q^{7}+\cdots\)
6034.2.a.g	$6034$	$2$	6034.a	1.a	$1$	$2$	$2$	$48.182$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(4\)	\(-5\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+(-2-\beta )q^{5}-2q^{6}+\cdots\)
6034.2.a.h	$6034$	$2$	6034.a	1.a	$1$	$2$	$2$	$48.182$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{7}+\cdots\)
6034.2.a.i	$6034$	$2$	6034.a	1.a	$1$	$2$	$2$	$48.182$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(4\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
6034.2.a.j	$6034$	$2$	6034.a	1.a	$1$	$4$	$4$	$48.182$	4.4.10273.1	None	✓	$1$	$1$	\(-4\)	\(-2\)	\(1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{3}q^{5}+\cdots\)
6034.2.a.k	$6034$	$2$	6034.a	1.a	$1$	$20$	$20$	$48.182$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(-20\)	\(3\)	\(-3\)	\(20\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{15}q^{5}-\beta _{1}q^{6}+\cdots\)
6034.2.a.l	$6034$	$2$	6034.a	1.a	$1$	$20$	$20$	$48.182$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(20\)	\(-3\)	\(-10\)	\(-20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{7})q^{5}+\cdots\)
6034.2.a.m	$6034$	$2$	6034.a	1.a	$1$	$21$	$21$	$48.182$		None	✓	$1$	$1$	\(21\)	\(-6\)	\(-11\)	\(21\)		$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
6034.2.a.n	$6034$	$2$	6034.a	1.a	$1$	$24$	$24$	$48.182$		None	✓	$1$	$0$	\(-24\)	\(7\)	\(8\)	\(-24\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6034.2.a.o	$6034$	$2$	6034.a	1.a	$1$	$25$	$25$	$48.182$		None	✓	$1$	$1$	\(-25\)	\(-4\)	\(0\)	\(-25\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6034.2.a.p	$6034$	$2$	6034.a	1.a	$1$	$27$	$27$	$48.182$		None	✓	$1$	$0$	\(-27\)	\(4\)	\(9\)	\(27\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
6034.2.a.q	$6034$	$2$	6034.a	1.a	$1$	$31$	$31$	$48.182$		None	✓	$1$	$0$	\(31\)	\(2\)	\(13\)	\(31\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
6034.2.a.r	$6034$	$2$	6034.a	1.a	$1$	$31$	$31$	$48.182$		None	✓	$1$	$0$	\(31\)	\(7\)	\(15\)	\(-31\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(431))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3017))\)\(^{\oplus 2}\)