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

• Label: 495.2.k
• Level: $495$
• Weight: $2$
• Character orbit: 495.k
• Rep. character: $\chi_{495}(208,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	160	64	96
Cusp forms	128	56	72
Eisenstein series	32	8	24

Trace form

56 * q + 4 * q^11 - 60 * q^16 + 16 * q^20 + 4 * q^22 + 18 * q^23 - 18 * q^25 + 40 * q^26 - 24 * q^31 + 30 * q^37 + 16 * q^38 + 12 * q^47 - 8 * q^53 - 10 * q^55 - 160 * q^56 + 24 * q^58 - 90 * q^67 + 80 * q^70 + 76 * q^71 - 24 * q^77 + 128 * q^80 + 40 * q^82 - 80 * q^86 + 20 * q^88 - 128 * q^92 + 18 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
495.2.k.a	$495$	$2$	495.k	55.e	$4$	$4$	$2$	$3.953$	\(\Q(i, \sqrt{11})\)	\(\Q(\sqrt{-11}) \)					55.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q-2\beta _{2}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
495.2.k.b	$495$	$2$	495.k	55.e	$4$	$4$	$2$	$3.953$	\(\Q(i, \sqrt{10})\)	None					55.2.e.a	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(2+\beta _{2})q^{5}+\beta _{3}q^{8}+\cdots\)
495.2.k.c	$495$	$2$	495.k	55.e	$4$	$24$	$12$	$3.953$		None					165.2.j.a	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
495.2.k.d	$495$	$2$	495.k	55.e	$4$	$24$	$12$	$3.953$		None		✓			495.2.k.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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