Space of modular forms of level 575, weight 3, and Character 575.c

• Label: 575.3.c
• Level: $575$
• Weight: $3$
• Character orbit: 575.c
• Rep. character: $\chi_{575}(574,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	575.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(575, [\chi])\).

	Total	New	Old
Modular forms	126	74	52
Cusp forms	114	70	44
Eisenstein series	12	4	8

Trace form

\( 70 q - 124 q^{4} + 20 q^{6} - 182 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(575, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
575.3.c.a	$575$	$3$	575.c	115.c	$2$	$6$	$6$	$15.668$	6.0.24681024.1	\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}-\beta _{5})q^{2}+(-2\beta _{1}-\beta _{5})q^{3}+\cdots\)
575.3.c.b	$575$	$3$	575.c	115.c	$2$	$12$	$12$	$15.668$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	\(\Q(\sqrt{-23}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{2}+(-\beta _{5}-\beta _{6}+\beta _{11})q^{3}+(-4+\cdots)q^{4}+\cdots\)
575.3.c.c	$575$	$3$	575.c	115.c	$2$	$12$	$12$	$15.668$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}+\beta _{8}q^{3}+3q^{4}+\beta _{2}q^{6}-\beta _{4}q^{7}+\cdots\)
575.3.c.d	$575$	$3$	575.c	115.c	$2$	$20$	$20$	$15.668$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{2}+\beta _{12}q^{3}+(-3+\beta _{9})q^{4}+\cdots\)
575.3.c.e	$575$	$3$	575.c	115.c	$2$	$20$	$20$	$15.668$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+\beta _{12}q^{3}+(-1+\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(575, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(575, [\chi]) \cong \)