Space of modular forms of level 9100, weight 2, and trivial character

• Label: 9100.2.a
• Level: $9100$
• Weight: $2$
• Character orbit: 9100.a
• Rep. character: $\chi_{9100}(1,\cdot)$
• Character field: $\Q$
• Dimension: $114$
• Newform subspaces: $45$
• Sturm bound: $3360$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9100 = 2^{2} \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9100.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 45 \)
Sturm bound:			\(3360\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9100))\).

	Total	New	Old
Modular forms	1716	114	1602
Cusp forms	1645	114	1531
Eisenstein series	71	0	71

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

\(2\)	\(5\)	\(7\)	\(13\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(14\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(13\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(13\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(14\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(14\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(16\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(16\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(14\)
Plus space				\(+\)	\(54\)
Minus space				\(-\)	\(60\)

Trace form

\( 114 q + 8 q^{3} + 122 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9100))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	5	7	13
9100.2.a.a	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{7}+6q^{9}-6q^{11}-q^{13}+\cdots\)
9100.2.a.b	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}+q^{11}+q^{13}-2q^{17}+\cdots\)
9100.2.a.c	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
9100.2.a.d	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}-q^{13}+6q^{17}+\cdots\)
9100.2.a.e	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
9100.2.a.f	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓				364.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}-2q^{11}+q^{13}+4q^{17}+\cdots\)
9100.2.a.g	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.g	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+3q^{11}+q^{13}+4q^{17}+\cdots\)
9100.2.a.h	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.g	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+3q^{11}-q^{13}-4q^{17}+\cdots\)
9100.2.a.i	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots\)
9100.2.a.j	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots\)
9100.2.a.k	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.c	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
9100.2.a.l	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓				364.2.a.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
9100.2.a.m	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}+q^{11}-q^{13}+2q^{17}+\cdots\)
9100.2.a.n	$9100$	$2$	9100.a	1.a	$1$	$1$	$1$	$72.664$	\(\Q\)	None	✓	✓			9100.2.a.a	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{7}+6q^{9}-6q^{11}+q^{13}+\cdots\)
9100.2.a.o	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{3}) \)	None	✓				364.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{7}+(1-2\beta )q^{9}+(3+\cdots)q^{11}+\cdots\)
9100.2.a.p	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{3}) \)	None	✓				1820.2.a.f	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{7}+(1-2\beta )q^{9}+(3+\cdots)q^{11}+\cdots\)
9100.2.a.q	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{3}) \)	None	✓				1820.2.g.a	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{7}+(1-2\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
9100.2.a.r	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{3}) \)	None	✓				1820.2.g.b	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{7}+(1-2\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
9100.2.a.s	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{5}) \)	None	✓				1820.2.g.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{7}+(-2+\beta )q^{9}+(-4+2\beta )q^{11}+\cdots\)
9100.2.a.t	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{21}) \)	None	✓				1820.2.g.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{7}+(2+\beta )q^{9}-2\beta q^{11}+\cdots\)
9100.2.a.u	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{5}) \)	None	✓				1820.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots\)
9100.2.a.v	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{6}) \)	None	✓				364.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{7}+3q^{9}+(4+\beta )q^{11}+q^{13}+\cdots\)
9100.2.a.w	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{13}) \)	None	✓				1820.2.a.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{7}+\beta q^{9}-2q^{11}+q^{13}+\cdots\)
9100.2.a.x	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{5}) \)	None	✓				1820.2.g.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{7}+(-2+\beta )q^{9}+(-4+2\beta )q^{11}+\cdots\)
9100.2.a.y	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{5}) \)	None	✓				1820.2.a.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{7}+(-2+\beta )q^{9}-2\beta q^{11}+\cdots\)
9100.2.a.z	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{21}) \)	None	✓				1820.2.g.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{7}+(2+\beta )q^{9}-2\beta q^{11}+\cdots\)
9100.2.a.ba	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{3}) \)	None	✓				1820.2.g.b	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{7}+(1+2\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
9100.2.a.bb	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{3}) \)	None	✓				1820.2.g.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{7}+(1+2\beta )q^{9}+(-1+\cdots)q^{11}+\cdots\)
9100.2.a.bc	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{5}) \)	None	✓				1820.2.a.b	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{7}+(-1+3\beta )q^{9}-2q^{11}+\cdots\)
9100.2.a.bd	$9100$	$2$	9100.a	1.a	$1$	$2$	$2$	$72.664$	\(\Q(\sqrt{13}) \)	None	✓				1820.2.a.a	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{7}+(1+3\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
9100.2.a.be	$9100$	$2$	9100.a	1.a	$1$	$3$	$3$	$72.664$	3.3.473.1	None	✓	✓			9100.2.a.be	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{7}+(1-2\beta _{1}+\beta _{2})q^{9}+\cdots\)
9100.2.a.bf	$9100$	$2$	9100.a	1.a	$1$	$3$	$3$	$72.664$	3.3.568.1	None	✓	✓			9100.2.a.bf	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
9100.2.a.bg	$9100$	$2$	9100.a	1.a	$1$	$3$	$3$	$72.664$	3.3.473.1	None	✓	✓	✓		9100.2.a.bg	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{7}+(3+\beta _{1}-\beta _{2})q^{9}+(2+\cdots)q^{11}+\cdots\)
9100.2.a.bh	$9100$	$2$	9100.a	1.a	$1$	$3$	$3$	$72.664$	3.3.473.1	None	✓	✓	✓		9100.2.a.bg	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{7}+(3+\beta _{1}-\beta _{2})q^{9}+(2+\cdots)q^{11}+\cdots\)
9100.2.a.bi	$9100$	$2$	9100.a	1.a	$1$	$3$	$3$	$72.664$	3.3.568.1	None	✓	✓			9100.2.a.bf	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{7}+(2+\beta _{2})q^{9}-\beta _{1}q^{11}+\cdots\)
9100.2.a.bj	$9100$	$2$	9100.a	1.a	$1$	$3$	$3$	$72.664$	3.3.473.1	None	✓	✓			9100.2.a.be	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{7}+(1-2\beta _{1}+\beta _{2})q^{9}+\cdots\)
9100.2.a.bk	$9100$	$2$	9100.a	1.a	$1$	$4$	$4$	$72.664$	4.4.50908.1	None	✓				1820.2.a.i	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-q^{7}+(2-\beta _{1}+\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots\)
9100.2.a.bl	$9100$	$2$	9100.a	1.a	$1$	$4$	$4$	$72.664$	4.4.47353.1	None	✓	✓			9100.2.a.bl	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{7}+(2+\beta _{2})q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
9100.2.a.bm	$9100$	$2$	9100.a	1.a	$1$	$4$	$4$	$72.664$	4.4.47353.1	None	✓	✓			9100.2.a.bl	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{7}+(2+\beta _{2})q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
9100.2.a.bn	$9100$	$2$	9100.a	1.a	$1$	$4$	$4$	$72.664$	4.4.30972.1	None	✓				1820.2.a.h	$1$	$1$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
9100.2.a.bo	$9100$	$2$	9100.a	1.a	$1$	$4$	$4$	$72.664$	4.4.27004.1	None	✓		✓		1820.2.a.g	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
9100.2.a.bp	$9100$	$2$	9100.a	1.a	$1$	$5$	$5$	$72.664$	5.5.897852.1	None	✓	✓	✓		9100.2.a.bp	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-5\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{7}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
9100.2.a.bq	$9100$	$2$	9100.a	1.a	$1$	$5$	$5$	$72.664$	5.5.897852.1	None	✓	✓			9100.2.a.bp	$1$	$0$	\(0\)	\(1\)	\(0\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{7}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
9100.2.a.br	$9100$	$2$	9100.a	1.a	$1$	$10$	$10$	$72.664$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		1820.2.g.e	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(10\)		$-$	$-$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{7}+(2+\beta _{2})q^{9}+(1-\beta _{7}+\cdots)q^{11}+\cdots\)
9100.2.a.bs	$9100$	$2$	9100.a	1.a	$1$	$10$	$10$	$72.664$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		1820.2.g.e	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-10\)		$-$	$-$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{7}+(2+\beta _{2})q^{9}+(1-\beta _{7}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9100)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(650))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(910))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1820))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4550))\)\(^{\oplus 2}\)