Space of modular forms of level 265, weight 2, and Character 265.m

• Label: 265.2.m
• Level: $265$
• Weight: $2$
• Character orbit: 265.m
• Rep. character: $\chi_{265}(6,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $216$
• Newform subspaces: $1$
• Sturm bound: $54$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 265 = 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	265.m (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(54\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(265, [\chi])\).

	Total	New	Old
Modular forms	360	216	144
Cusp forms	312	216	96
Eisenstein series	48	0	48

Trace form

216 * q + 18 * q^4 + 4 * q^6 - 4 * q^7 - 52 * q^8 + 18 * q^9 - 20 * q^10 + 8 * q^11 + 8 * q^13 + 4 * q^15 - 42 * q^16 - 20 * q^17 - 52 * q^22 - 80 * q^24 + 18 * q^25 - 26 * q^26 - 12 * q^28 - 68 * q^29 - 52 * q^31 - 38 * q^36 + 20 * q^37 - 216 * q^38 - 30 * q^40 + 26 * q^41 + 2 * q^42 - 56 * q^43 + 116 * q^44 - 52 * q^45 - 4 * q^46 + 46 * q^47 + 16 * q^49 + 104 * q^51 + 160 * q^52 + 24 * q^53 + 68 * q^54 + 130 * q^56 + 100 * q^57 + 4 * q^59 - 12 * q^60 - 78 * q^61 + 20 * q^62 - 90 * q^63 + 158 * q^64 - 76 * q^66 + 26 * q^67 + 16 * q^68 - 52 * q^69 - 28 * q^70 - 260 * q^72 - 52 * q^73 - 26 * q^74 - 110 * q^77 + 84 * q^78 - 260 * q^79 - 104 * q^80 + 22 * q^81 + 80 * q^82 - 234 * q^84 - 208 * q^86 - 78 * q^88 - 24 * q^89 + 114 * q^90 + 68 * q^91 - 4 * q^93 + 130 * q^94 + 76 * q^95 + 124 * q^96 + 20 * q^97 - 26 * q^98 + 94 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(265, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
265.2.m.a	$265$	$2$	265.m	53.e	$26$	$216$	$18$	$2.116$		None		✓	✓	✓	265.2.m.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{26}]$

Decomposition of \(S_{2}^{\mathrm{old}}(265, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(265, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 2}\)