Space of modular forms of level 260, weight 2, and Character 260.o

• Label: 260.2.o
• Level: $260$
• Weight: $2$
• Character orbit: 260.o
• Rep. character: $\chi_{260}(27,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$260 = 2^{2} \cdot 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	260.o (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$20$
Character field:			$\Q(i)$
Newform subspaces:			$1$
Sturm bound:			$84$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(260, [\chi])$.

	Total	New	Old
Modular forms	92	72	20
Cusp forms	76	72	4
Eisenstein series	16	0	16

Trace form

72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(260, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
260.2.o.a	$260$	$2$	260.o	20.e	$4$	$72$	$36$	$2.076$		None		✓	✓	✓	260.2.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{4}]$

Decomposition of $S_{2}^{\mathrm{old}}(260, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(260, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(20, [\chi])$$^{\oplus 2}$