Space of modular forms of level 475, weight 2, and Character 475.e

• Label: 475.2.e
• Level: $475$
• Weight: $2$
• Character orbit: 475.e
• Rep. character: $\chi_{475}(26,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $8$
• Sturm bound: $100$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(100\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).

	Total	New	Old
Modular forms	112	68	44
Cusp forms	88	56	32
Eisenstein series	24	12	12

Trace form

\( 56 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 6 q^{6} + 12 q^{7} - 12 q^{8} - 22 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
475.2.e.a	$475$	$2$	475.e	19.c	$3$	$2$	$1$	$3.793$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-4q^{7}+\cdots\)
475.2.e.b	$475$	$2$	475.e	19.c	$3$	$2$	$1$	$3.793$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+4q^{7}+\cdots\)
475.2.e.c	$475$	$2$	475.e	19.c	$3$	$2$	$1$	$3.793$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+4q^{7}+3\zeta_{6}q^{9}+\cdots\)
475.2.e.d	$475$	$2$	475.e	19.c	$3$	$6$	$3$	$3.793$	6.0.3518667.1	None		$2$	$0$	\(1\)	\(1\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
475.2.e.e	$475$	$2$	475.e	19.c	$3$	$8$	$4$	$3.793$	8.0.4601315889.1	None		$2$	$0$	\(1\)	\(3\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{7}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
475.2.e.f	$475$	$2$	475.e	19.c	$3$	$12$	$6$	$3.793$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-3\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{7}+\beta _{8})q^{2}+(1-\beta _{1}+\beta _{2}+\beta _{9}+\cdots)q^{3}+\cdots\)
475.2.e.g	$475$	$2$	475.e	19.c	$3$	$12$	$6$	$3.793$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\beta _{8}+\cdots)q^{4}+\cdots\)
475.2.e.h	$475$	$2$	475.e	19.c	$3$	$12$	$6$	$3.793$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(2\)	\(3\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{7}-\beta _{8})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(475, [\chi]) \cong \)