Space of modular forms of level 460, weight 2, and Character 460.e

• Label: 460.2.e
• Level: $460$
• Weight: $2$
• Character orbit: 460.e
• Rep. character: $\chi_{460}(91,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$460 = 2^{2} \cdot 5 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	460.e (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$92$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$144$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(460, [\chi])$.

	Total	New	Old
Modular forms	76	48	28
Cusp forms	68	48	20
Eisenstein series	8	0	8

Trace form

48 * q + 4 * q^2 - 2 * q^6 - 2 * q^8 - 48 * q^9 - 6 * q^12 + 24 * q^16 - 26 * q^18 - 4 * q^24 - 48 * q^25 + 14 * q^26 - 40 * q^29 - 16 * q^32 + 42 * q^36 + 8 * q^41 - 44 * q^46 + 14 * q^48 + 56 * q^49 - 4 * q^50 + 50 * q^52 + 2 * q^54 + 26 * q^58 - 30 * q^62 + 30 * q^64 - 4 * q^69 - 110 * q^72 + 154 * q^78 + 8 * q^81 - 22 * q^82 - 32 * q^85 + 64 * q^92 - 80 * q^93 - 6 * q^94 - 6 * q^96 + 44 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(460, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
460.2.e.a	$460$	$2$	460.e	92.b	$2$	$16$	$16$	$3.673$	16.0.$\cdots$.3	None		✓			460.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{2}+\beta _{8})q^{4}+\cdots$
460.2.e.b	$460$	$2$	460.e	92.b	$2$	$32$	$32$	$3.673$		None		✓	✓		460.2.e.b	$4$	$0$	$4$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{2}^{\mathrm{old}}(460, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(460, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(92, [\chi])$$^{\oplus 2}$