Space of modular forms of level 3234, weight 2, and trivial character

• Label: 3234.2.a
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.a
• Rep. character: $\chi_{3234}(1,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $39$
• Sturm bound: $1344$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 39 \)
Sturm bound:			\(1344\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3234))\).

	Total	New	Old
Modular forms	704	68	636
Cusp forms	641	68	573
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.

\(2\)	\(3\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(5\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(1\)
Plus space				\(+\)	\(24\)
Minus space				\(-\)	\(44\)

Trace form

68 * q + 2 * q^2 - 2 * q^3 + 68 * q^4 + 4 * q^5 + 2 * q^8 + 68 * q^9 + 4 * q^10 - 2 * q^12 + 68 * q^16 + 12 * q^17 + 2 * q^18 - 4 * q^19 + 4 * q^20 + 2 * q^22 - 4 * q^23 + 52 * q^25 + 16 * q^26 - 2 * q^27 - 12 * q^29 - 24 * q^31 + 2 * q^32 - 2 * q^33 + 68 * q^36 + 56 * q^37 - 4 * q^38 + 36 * q^39 + 4 * q^40 + 12 * q^41 + 12 * q^43 + 4 * q^45 + 12 * q^47 - 2 * q^48 + 62 * q^50 - 8 * q^51 + 60 * q^53 + 44 * q^57 + 64 * q^58 - 8 * q^59 + 24 * q^61 + 16 * q^62 + 68 * q^64 + 72 * q^65 - 4 * q^66 + 40 * q^67 + 12 * q^68 - 4 * q^69 + 4 * q^71 + 2 * q^72 + 24 * q^73 + 68 * q^74 - 6 * q^75 - 4 * q^76 - 20 * q^78 + 52 * q^79 + 4 * q^80 + 68 * q^81 - 8 * q^82 + 16 * q^83 + 56 * q^85 - 20 * q^86 - 8 * q^87 + 2 * q^88 + 24 * q^89 + 4 * q^90 - 4 * q^92 + 64 * q^93 + 8 * q^94 - 32 * q^95 + 16 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3234))\) 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
3234.2.a.a	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.a	$1$	$0$	\(-1\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.b	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.a.d	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.c	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.d	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.d	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				66.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.e	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓	✓			3234.2.a.e	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.f	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.b	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.g	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.c	$1$	$0$	\(-1\)	\(-1\)	\(3\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.h	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.c	$1$	$0$	\(-1\)	\(1\)	\(-3\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.i	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.a.c	$1$	$0$	\(-1\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.j	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.d	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.k	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.l	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.b	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.m	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓	✓			3234.2.a.e	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.n	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.o	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.i.a	$1$	$0$	\(-1\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.p	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.a.g	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.q	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.a.f	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
3234.2.a.r	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓	✓			3234.2.a.r	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.s	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				66.2.a.c	$1$	$0$	\(1\)	\(-1\)	\(4\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.t	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				66.2.a.b	$1$	$0$	\(1\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.u	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓	✓	✓	✓	3234.2.a.r	$1$	$1$	\(1\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.v	$3234$	$2$	3234.a	1.a	$1$	$1$	$1$	$25.824$	\(\Q\)	None	✓				462.2.a.e	$1$	$0$	\(1\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.w	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{7}) \)	None	✓				462.2.i.e	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.x	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{3}) \)	None	✓		✓		462.2.a.h	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.y	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{2}) \)	None	✓	✓			3234.2.a.y	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.z	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		3234.2.a.y	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
3234.2.a.ba	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{7}) \)	None	✓		✓		462.2.i.e	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.bb	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		3234.2.a.bb	$1$	$1$	\(2\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
3234.2.a.bc	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{2}) \)	None	✓	✓			3234.2.a.bc	$1$	$0$	\(2\)	\(-2\)	\(4\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.bd	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	3234.2.a.bc	$1$	$1$	\(2\)	\(2\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.be	$3234$	$2$	3234.a	1.a	$1$	$2$	$2$	$25.824$	\(\Q(\sqrt{5}) \)	None	✓	✓			3234.2.a.bb	$1$	$0$	\(2\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
3234.2.a.bf	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.2700.1	None	✓		✓		462.2.i.g	$1$	$0$	\(3\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.bg	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.621.1	None	✓		✓		462.2.i.f	$1$	$0$	\(3\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+q^{8}+\cdots\)
3234.2.a.bh	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.2700.1	None	✓		✓		462.2.i.g	$1$	$0$	\(3\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.bi	$3234$	$2$	3234.a	1.a	$1$	$3$	$3$	$25.824$	3.3.621.1	None	✓				462.2.i.f	$1$	$0$	\(3\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+q^{8}+\cdots\)
3234.2.a.bj	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.14336.1	None	✓	✓	✓		3234.2.a.bj	$1$	$1$	\(-4\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}-q^{8}+\cdots\)
3234.2.a.bk	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.14336.1	None	✓	✓	✓		3234.2.a.bj	$1$	$0$	\(-4\)	\(4\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}-q^{8}+\cdots\)
3234.2.a.bl	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.4352.1	None	✓	✓	✓	✓	3234.2.a.bl	$1$	$1$	\(4\)	\(-4\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{3})q^{5}-q^{6}+\cdots\)
3234.2.a.bm	$3234$	$2$	3234.a	1.a	$1$	$4$	$4$	$25.824$	4.4.4352.1	None	✓	✓	✓		3234.2.a.bl	$1$	$0$	\(4\)	\(4\)	\(4\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1+\beta _{3})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3234))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3234)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 2}\)