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

• Label: 3150.2.d
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.d
• Rep. character: $\chi_{3150}(3149,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $1440$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1440\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(11\), \(13\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	768	48	720
Cusp forms	672	48	624
Eisenstein series	96	0	96

Trace form

\( 48 q + 48 q^{4} + O(q^{10}) \)

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.d.a	$3150$	$2$	3150.d	105.g	$2$	$8$	$8$	$25.153$	8.0.7442857984.4	None		$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}-\beta _{3}q^{11}+\cdots\)
3150.2.d.b	$3150$	$2$	3150.d	105.g	$2$	$8$	$8$	$25.153$	8.0.40960000.1	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+(\beta _{1}+\beta _{2})q^{7}-q^{8}+\beta _{2}q^{11}+\cdots\)
3150.2.d.c	$3150$	$2$	3150.d	105.g	$2$	$8$	$8$	$25.153$	8.0.7442857984.4	None		$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}-\beta _{3}q^{11}+\cdots\)
3150.2.d.d	$3150$	$2$	3150.d	105.g	$2$	$8$	$8$	$25.153$	8.0.7442857984.4	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}-\beta _{3}q^{11}+\cdots\)
3150.2.d.e	$3150$	$2$	3150.d	105.g	$2$	$8$	$8$	$25.153$	8.0.40960000.1	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+q^{8}+\beta _{2}q^{11}+\cdots\)
3150.2.d.f	$3150$	$2$	3150.d	105.g	$2$	$8$	$8$	$25.153$	8.0.7442857984.4	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}-\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)