Space of modular forms of level 3150, weight 3, and Character 3150.e

• Label: 3150.3.e
• Level: $3150$
• Weight: $3$
• Character orbit: 3150.e
• Rep. character: $\chi_{3150}(701,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $11$
• Sturm bound: $2160$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	3150.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2160\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3150, [\chi])\).

	Total	New	Old
Modular forms	1488	76	1412
Cusp forms	1392	76	1316
Eisenstein series	96	0	96

Trace form

\( 76 q - 152 q^{4} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(3150, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3150.3.e.a	$3150$	$3$	3150.e	3.b	$2$	$4$	$4$	$85.831$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}-\beta _{3}q^{7}+2\beta _{2}q^{8}+\cdots\)
3150.3.e.b	$3150$	$3$	3150.e	3.b	$2$	$4$	$4$	$85.831$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}-\beta _{3}q^{7}-2\beta _{2}q^{8}+\cdots\)
3150.3.e.c	$3150$	$3$	3150.e	3.b	$2$	$4$	$4$	$85.831$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}+\beta _{3}q^{7}+2\beta _{2}q^{8}+\cdots\)
3150.3.e.d	$3150$	$3$	3150.e	3.b	$2$	$4$	$4$	$85.831$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}+\beta _{3}q^{7}-2\beta _{2}q^{8}+\cdots\)
3150.3.e.e	$3150$	$3$	3150.e	3.b	$2$	$4$	$4$	$85.831$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\)
3150.3.e.f	$3150$	$3$	3150.e	3.b	$2$	$8$	$8$	$85.831$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-2q^{4}+\beta _{2}q^{7}+2\beta _{4}q^{8}+\cdots\)
3150.3.e.g	$3150$	$3$	3150.e	3.b	$2$	$8$	$8$	$85.831$	8.0.\(\cdots\).30	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}+\beta _{1}q^{7}+2\beta _{2}q^{8}+\cdots\)
3150.3.e.h	$3150$	$3$	3150.e	3.b	$2$	$8$	$8$	$85.831$	8.0.\(\cdots\).30	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-2q^{4}-\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots\)
3150.3.e.i	$3150$	$3$	3150.e	3.b	$2$	$8$	$8$	$85.831$	8.0.\(\cdots\).4	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-2q^{4}-\beta _{1}q^{7}+2\beta _{3}q^{8}+\cdots\)
3150.3.e.j	$3150$	$3$	3150.e	3.b	$2$	$12$	$12$	$85.831$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-2q^{4}-\beta _{4}q^{7}-2\beta _{5}q^{8}+\cdots\)
3150.3.e.k	$3150$	$3$	3150.e	3.b	$2$	$12$	$12$	$85.831$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-2q^{4}+\beta _{4}q^{7}+2\beta _{5}q^{8}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)