Space of modular forms of level 495, weight 4, and Character 495.c

• Label: 495.4.c
• Level: $495$
• Weight: $4$
• Character orbit: 495.c
• Rep. character: $\chi_{495}(199,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	495.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(495, [\chi])\).

	Total	New	Old
Modular forms	224	76	148
Cusp forms	208	76	132
Eisenstein series	16	0	16

Trace form

\( 76 q - 324 q^{4} + 18 q^{5} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(495, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.4.c.a	$495$	$4$	495.c	5.b	$2$	$6$	$6$	$29.206$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
495.4.c.b	$495$	$4$	495.c	5.b	$2$	$10$	$10$	$29.206$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{3}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-6+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
495.4.c.c	$495$	$4$	495.c	5.b	$2$	$14$	$14$	$29.206$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-6+\beta _{2})q^{4}+(1+\beta _{8})q^{5}+\cdots\)
495.4.c.d	$495$	$4$	495.c	5.b	$2$	$14$	$14$	$29.206$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{8}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-2+\beta _{1})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
495.4.c.e	$495$	$4$	495.c	5.b	$2$	$16$	$16$	$29.206$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-5+\beta _{2})q^{4}+\beta _{7}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
495.4.c.f	$495$	$4$	495.c	5.b	$2$	$16$	$16$	$29.206$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-5+\beta _{2})q^{4}+\beta _{7}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(495, [\chi]) \cong \)