Space of modular forms of level 1575, weight 2, and Character 1575.b

• Label: 1575.2.b
• Level: $1575$
• Weight: $2$
• Character orbit: 1575.b
• Rep. character: $\chi_{1575}(251,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $8$
• Sturm bound: $480$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(480\)
Trace bound:			\(22\)
Distinguishing \(T_p\):			\(2\), \(37\), \(47\), \(67\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

	Total	New	Old
Modular forms	264	52	212
Cusp forms	216	52	164
Eisenstein series	48	0	48

Trace form

\( 52 q - 56 q^{4} - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1575.2.b.a	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.b.b	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
1575.2.b.c	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
1575.2.b.d	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{2}q^{7}-2\beta _{1}q^{8}-\beta _{1}q^{11}+\cdots\)
1575.2.b.e	$1575$	$2$	1575.b	21.c	$2$	$4$	$4$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{7}+2\beta _{1}q^{8}-\beta _{1}q^{11}+\cdots\)
1575.2.b.f	$1575$	$2$	1575.b	21.c	$2$	$8$	$8$	$12.576$	8.0.\(\cdots\).3	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{4}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.b.g	$1575$	$2$	1575.b	21.c	$2$	$8$	$8$	$12.576$	8.0.\(\cdots\).3	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{4}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.b.h	$1575$	$2$	1575.b	21.c	$2$	$16$	$16$	$12.576$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-1-\beta _{1})q^{4}-\beta _{8}q^{7}+(-\beta _{2}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)