Space of modular forms of level 3465, weight 2, and trivial character

• Label: 3465.2.a
• Level: $3465$
• Weight: $2$
• Character orbit: 3465.a
• Rep. character: $\chi_{3465}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $43$
• Sturm bound: $1152$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 3465 = 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3465.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 43 \)
Sturm bound:			\(1152\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(2\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3465))\).

	Total	New	Old
Modular forms	592	100	492
Cusp forms	561	100	461
Eisenstein series	31	0	31

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

\(3\)	\(5\)	\(7\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(8\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(6\)
Plus space				\(+\)	\(44\)
Minus space				\(-\)	\(56\)

Trace form

\( 100 q + 92 q^{4} - 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3465))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	7	11
3465.2.a.a	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
3465.2.a.b	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+q^{7}+3q^{8}+q^{10}+\cdots\)
3465.2.a.c	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+q^{7}+3q^{8}+q^{10}+\cdots\)
3465.2.a.d	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots\)
3465.2.a.e	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots\)
3465.2.a.f	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-q^{10}+\cdots\)
3465.2.a.g	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-q^{10}+\cdots\)
3465.2.a.h	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}-q^{7}+q^{11}-4q^{13}+\cdots\)
3465.2.a.i	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+q^{7}-q^{11}+4q^{16}+\cdots\)
3465.2.a.j	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+q^{7}+q^{11}-4q^{13}+\cdots\)
3465.2.a.k	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots\)
3465.2.a.l	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots\)
3465.2.a.m	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots\)
3465.2.a.n	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
3465.2.a.o	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
3465.2.a.p	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
3465.2.a.q	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}+q^{10}+\cdots\)
3465.2.a.r	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+q^{7}-2q^{10}+\cdots\)
3465.2.a.s	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+q^{7}-2q^{10}+\cdots\)
3465.2.a.t	$3465$	$2$	3465.a	1.a	$1$	$1$	$1$	$27.668$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots\)
3465.2.a.u	$3465$	$2$	3465.a	1.a	$1$	$2$	$2$	$27.668$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}-q^{7}+\cdots\)
3465.2.a.v	$3465$	$2$	3465.a	1.a	$1$	$2$	$2$	$27.668$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+q^{7}+\cdots\)
3465.2.a.w	$3465$	$2$	3465.a	1.a	$1$	$2$	$2$	$27.668$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{5}-q^{7}-2\beta q^{8}+\beta q^{10}+\cdots\)
3465.2.a.x	$3465$	$2$	3465.a	1.a	$1$	$2$	$2$	$27.668$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+q^{5}+q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
3465.2.a.y	$3465$	$2$	3465.a	1.a	$1$	$2$	$2$	$27.668$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+4q^{4}-q^{5}+q^{7}+2\beta q^{8}+\cdots\)
3465.2.a.z	$3465$	$2$	3465.a	1.a	$1$	$2$	$2$	$27.668$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}-q^{5}-q^{7}+(4+\beta )q^{8}+\cdots\)
3465.2.a.ba	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.148.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+q^{7}+\cdots\)
3465.2.a.bb	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.316.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
3465.2.a.bc	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.316.1	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
3465.2.a.bd	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}-q^{7}+\cdots\)
3465.2.a.be	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+q^{7}+\cdots\)
3465.2.a.bf	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}-q^{7}+\cdots\)
3465.2.a.bg	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+q^{7}+\cdots\)
3465.2.a.bh	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.148.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
3465.2.a.bi	$3465$	$2$	3465.a	1.a	$1$	$3$	$3$	$27.668$	3.3.148.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
3465.2.a.bj	$3465$	$2$	3465.a	1.a	$1$	$4$	$4$	$27.668$	4.4.7232.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{2}-\beta _{3})q^{4}-q^{5}+q^{7}+\cdots\)
3465.2.a.bk	$3465$	$2$	3465.a	1.a	$1$	$4$	$4$	$27.668$	4.4.11348.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots\)
3465.2.a.bl	$3465$	$2$	3465.a	1.a	$1$	$4$	$4$	$27.668$	4.4.13448.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}-q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
3465.2.a.bm	$3465$	$2$	3465.a	1.a	$1$	$5$	$5$	$27.668$	5.5.352076.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(5\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
3465.2.a.bn	$3465$	$2$	3465.a	1.a	$1$	$6$	$6$	$27.668$	6.6.59342224.1	None	✓	$1$	$0$	\(-3\)	\(0\)	\(6\)	\(-6\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
3465.2.a.bo	$3465$	$2$	3465.a	1.a	$1$	$6$	$6$	$27.668$	6.6.498384144.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-6\)	\(6\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
3465.2.a.bp	$3465$	$2$	3465.a	1.a	$1$	$6$	$6$	$27.668$	6.6.498384144.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(6\)	\(6\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
3465.2.a.bq	$3465$	$2$	3465.a	1.a	$1$	$6$	$6$	$27.668$	6.6.59342224.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(-6\)	\(-6\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3465))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3465)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 2}\)