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

• Label: 3150.3.c
• Level: $3150$
• Weight: $3$
• Character orbit: 3150.c
• Rep. character: $\chi_{3150}(449,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $2160$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	3150.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(2160\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	1488	72	1416
Cusp forms	1392	72	1320
Eisenstein series	96	0	96

Trace form

\( 72 q + 144 q^{4} + O(q^{10}) \)

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.c.a	$3150$	$3$	3150.c	15.d	$2$	$8$	$8$	$85.831$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+2q^{4}+\beta _{1}q^{7}-2\beta _{6}q^{8}+\cdots\)
3150.3.c.b	$3150$	$3$	3150.c	15.d	$2$	$8$	$8$	$85.831$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+2q^{4}+\beta _{1}q^{7}-2\beta _{3}q^{8}+\cdots\)
3150.3.c.c	$3150$	$3$	3150.c	15.d	$2$	$8$	$8$	$85.831$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+2q^{4}-\beta _{1}q^{7}+2\beta _{6}q^{8}+\cdots\)
3150.3.c.d	$3150$	$3$	3150.c	15.d	$2$	$16$	$16$	$85.831$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+2q^{4}-\beta _{2}q^{7}-2\beta _{5}q^{8}+\cdots\)
3150.3.c.e	$3150$	$3$	3150.c	15.d	$2$	$16$	$16$	$85.831$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+2q^{4}-\beta _{10}q^{7}+2\beta _{2}q^{8}+\cdots\)
3150.3.c.f	$3150$	$3$	3150.c	15.d	$2$	$16$	$16$	$85.831$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+2q^{4}+\beta _{2}q^{7}-2\beta _{6}q^{8}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)