Space of modular forms of level 495, weight 2, and Character 495.n

• Label: 495.2.n
• Level: $495$
• Weight: $2$
• Character orbit: 495.n
• Rep. character: $\chi_{495}(91,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $80$
• Newform subspaces: $8$
• Sturm bound: $144$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(144\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(495, [\chi])\).

	Total	New	Old
Modular forms	320	80	240
Cusp forms	256	80	176
Eisenstein series	64	0	64

Trace form

\( 80 q - 2 q^{2} - 24 q^{4} - 4 q^{7} + 14 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(495, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.2.n.a	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.13140625.1	None		$2$	$0$	\(-4\)	\(0\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
495.2.n.b	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.819390625.1	None		$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{4}q^{2}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
495.2.n.c	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	\(\Q(\zeta_{15})\)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
495.2.n.d	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.13140625.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{4}+\cdots\)
495.2.n.e	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.13140625.1	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{6}-\beta _{7})q^{4}+\cdots\)
495.2.n.f	$495$	$2$	495.n	11.c	$5$	$8$	$2$	$3.953$	8.0.159390625.1	None		$2$	$0$	\(4\)	\(0\)	\(2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
495.2.n.g	$495$	$2$	495.n	11.c	$5$	$16$	$4$	$3.953$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{10}-\beta _{14}+\cdots)q^{2}+\cdots\)
495.2.n.h	$495$	$2$	495.n	11.c	$5$	$16$	$4$	$3.953$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{1}-\beta _{3}-\beta _{5}+\beta _{10}+\beta _{14}+\cdots)q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)