Space of modular forms of level 3696, weight 2, and trivial character

• Label: 3696.2.a
• Level: $3696$
• Weight: $2$
• Character orbit: 3696.a
• Rep. character: $\chi_{3696}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $42$
• Sturm bound: $1536$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3696 = 2^{4} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3696.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 42 \)
Sturm bound:			\(1536\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3696))\).

	Total	New	Old
Modular forms	792	60	732
Cusp forms	745	60	685
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(2\)
Plus space				\(+\)	\(24\)
Minus space				\(-\)	\(36\)

Trace form

60 * q - 8 * q^5 + 60 * q^9 - 8 * q^13 - 8 * q^15 + 8 * q^17 - 16 * q^19 + 68 * q^25 - 8 * q^29 - 16 * q^31 - 8 * q^37 + 8 * q^41 - 8 * q^45 + 60 * q^49 - 16 * q^51 - 8 * q^53 + 24 * q^61 + 48 * q^65 + 24 * q^67 + 32 * q^69 + 48 * q^71 + 40 * q^73 - 16 * q^79 + 60 * q^81 + 48 * q^83 + 16 * q^85 + 24 * q^89 + 24 * q^91 + 48 * q^95 - 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3696))\) 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	3	7	11
3696.2.a.a	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
3696.2.a.b	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}-7q^{13}+\cdots\)
3696.2.a.c	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
3696.2.a.d	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}+3q^{13}+\cdots\)
3696.2.a.e	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
3696.2.a.f	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-5q^{13}+\cdots\)
3696.2.a.g	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3696.2.a.h	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3696.2.a.i	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				462.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-2q^{19}+\cdots\)
3696.2.a.j	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				462.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+q^{11}+6q^{13}+4q^{17}+\cdots\)
3696.2.a.k	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-5q^{13}+\cdots\)
3696.2.a.l	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.k	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+3q^{13}+\cdots\)
3696.2.a.m	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				462.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
3696.2.a.n	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.l	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
3696.2.a.o	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
3696.2.a.p	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				462.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
3696.2.a.q	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3696.2.a.r	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3696.2.a.s	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				462.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
3696.2.a.t	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				231.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
3696.2.a.u	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
3696.2.a.v	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
3696.2.a.w	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3696.2.a.x	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-8q^{17}+\cdots\)
3696.2.a.y	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				462.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+q^{11}-2q^{13}-4q^{17}+\cdots\)
3696.2.a.z	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				924.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3696.2.a.ba	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				1848.2.a.d	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
3696.2.a.bb	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	\(\Q\)	None	✓				462.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
3696.2.a.bc	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{3}) \)	None	✓				462.2.a.h	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
3696.2.a.bd	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{41}) \)	None	✓		✓		1848.2.a.s	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}+q^{9}-q^{11}-\beta q^{13}+\cdots\)
3696.2.a.be	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{5}) \)	None	✓				231.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
3696.2.a.bf	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{33}) \)	None	✓		✓		1848.2.a.o	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
3696.2.a.bg	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{17}) \)	None	✓				1848.2.a.m	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
3696.2.a.bh	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{17}) \)	None	✓				1848.2.a.n	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
3696.2.a.bi	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{17}) \)	None	✓				1848.2.a.p	$1$	$0$	\(0\)	\(2\)	\(1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots\)
3696.2.a.bj	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{17}) \)	None	✓		✓		1848.2.a.r	$1$	$0$	\(0\)	\(2\)	\(3\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
3696.2.a.bk	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{17}) \)	None	✓				1848.2.a.q	$1$	$0$	\(0\)	\(2\)	\(3\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
3696.2.a.bl	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	\(\Q(\sqrt{21}) \)	None	✓		✓		231.2.a.b	$1$	$0$	\(0\)	\(2\)	\(6\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3696.2.a.bm	$3696$	$2$	3696.a	1.a	$1$	$3$	$3$	$29.513$	3.3.568.1	None	✓		✓		1848.2.a.u	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}-q^{7}+q^{9}-q^{11}+\beta _{1}q^{13}+\cdots\)
3696.2.a.bn	$3696$	$2$	3696.a	1.a	$1$	$3$	$3$	$29.513$	3.3.961.1	None	✓		✓		1848.2.a.t	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+q^{11}+(1+\cdots)q^{13}+\cdots\)
3696.2.a.bo	$3696$	$2$	3696.a	1.a	$1$	$3$	$3$	$29.513$	3.3.229.1	None	✓		✓		231.2.a.e	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
3696.2.a.bp	$3696$	$2$	3696.a	1.a	$1$	$3$	$3$	$29.513$	3.3.837.1	None	✓		✓		231.2.a.d	$1$	$0$	\(0\)	\(3\)	\(0\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}-q^{11}-\beta _{2}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3696))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3696)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(924))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1848))\)\(^{\oplus 2}\)