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}$