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

• Label: 260.2.bn
• Level: $260$
• Weight: $2$
• Character orbit: 260.bn
• Rep. character: $\chi_{260}(11,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $112$
• 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.bn (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{12})\)
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	184	112	72
Cusp forms	152	112	40
Eisenstein series	32	0	32

Trace form

112 * q + 12 * q^6 - 12 * q^8 + 56 * q^9 - 16 * q^14 - 24 * q^18 - 16 * q^20 + 16 * q^21 - 8 * q^24 - 44 * q^26 - 16 * q^28 - 48 * q^30 - 40 * q^32 - 20 * q^34 - 36 * q^36 - 16 * q^37 - 8 * q^41 + 64 * q^42 + 32 * q^44 + 12 * q^46 - 8 * q^48 - 144 * q^49 + 52 * q^52 - 32 * q^53 + 88 * q^54 - 96 * q^57 + 100 * q^58 - 16 * q^61 + 24 * q^62 + 8 * q^65 - 184 * q^66 - 24 * q^68 + 8 * q^70 - 124 * q^72 - 48 * q^73 - 32 * q^74 - 32 * q^76 - 52 * q^78 + 32 * q^80 - 56 * q^81 - 120 * q^82 - 148 * q^84 - 68 * q^86 + 60 * q^88 + 32 * q^89 + 40 * q^92 + 144 * q^93 - 8 * q^94 + 76 * q^96 + 80 * q^97 + 92 * 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.bn.a	$260$	$2$	260.bn	52.l	$12$	$112$	$28$	$2.076$		None		✓	✓	✓	260.2.bn.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(260, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)