Space of modular forms of level 3150, weight 2, and Character 3150.g

• Label: 3150.2.g
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.g
• Rep. character: $\chi_{3150}(2899,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $22$
• Sturm bound: $1440$
• Trace bound: $26$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(1440\)
Trace bound:			\(26\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

	Total	New	Old
Modular forms	768	44	724
Cusp forms	672	44	628
Eisenstein series	96	0	96

Trace form

\( 44 q - 44 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3150.2.g.a	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-6q^{11}+\cdots\)
3150.2.g.b	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4q^{11}+\cdots\)
3150.2.g.c	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.d	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.e	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.f	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-3q^{11}+\cdots\)
3150.2.g.g	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2q^{11}+\cdots\)
3150.2.g.h	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-2q^{11}+\cdots\)
3150.2.g.i	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+2iq^{13}+\cdots\)
3150.2.g.j	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4iq^{13}+\cdots\)
3150.2.g.k	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-iq^{13}+\cdots\)
3150.2.g.l	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2iq^{13}+\cdots\)
3150.2.g.m	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots\)
3150.2.g.n	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-iq^{13}+\cdots\)
3150.2.g.o	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots\)
3150.2.g.p	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+2q^{11}+\cdots\)
3150.2.g.q	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+4q^{11}+\cdots\)
3150.2.g.r	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.s	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.t	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+4q^{11}+\cdots\)
3150.2.g.u	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.v	$3150$	$2$	3150.g	5.b	$2$	$2$	$2$	$25.153$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+5q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)