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

• Label: 265.2.k
• Level: $265$
• Weight: $2$
• Character orbit: 265.k
• Rep. character: $\chi_{265}(16,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $216$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 265 = 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	265.k (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q(\zeta_{13})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	336	216	120
Cusp forms	288	216	72
Eisenstein series	48	0	48

Trace form

216 * q - 4 * q^2 - 26 * q^4 - 4 * q^6 - 4 * q^7 + 40 * q^8 - 18 * q^9 + 20 * q^10 - 16 * q^11 - 20 * q^12 - 8 * q^13 - 36 * q^14 - 4 * q^15 - 58 * q^16 - 20 * q^17 - 56 * q^18 - 12 * q^19 - 16 * q^21 + 20 * q^22 - 12 * q^23 + 56 * q^24 - 18 * q^25 - 10 * q^26 - 12 * q^27 - 28 * q^28 + 12 * q^29 - 16 * q^30 + 28 * q^31 - 48 * q^32 - 36 * q^33 - 20 * q^34 - 8 * q^35 - 110 * q^36 - 28 * q^37 + 192 * q^38 - 44 * q^39 - 30 * q^40 - 14 * q^41 + 126 * q^42 + 8 * q^43 + 36 * q^44 + 44 * q^45 - 52 * q^46 - 58 * q^47 - 112 * q^48 + 20 * q^49 - 4 * q^50 + 96 * q^52 - 48 * q^53 + 68 * q^54 - 8 * q^55 + 26 * q^56 + 36 * q^57 - 116 * q^58 + 44 * q^59 - 12 * q^60 + 54 * q^61 - 20 * q^62 - 22 * q^63 - 38 * q^64 - 12 * q^65 + 188 * q^66 - 42 * q^67 - 112 * q^68 - 124 * q^69 - 28 * q^70 - 72 * q^71 + 112 * q^72 + 20 * q^73 - 18 * q^74 - 172 * q^76 - 74 * q^77 - 180 * q^78 + 152 * q^79 + 88 * q^80 - 90 * q^81 - 128 * q^82 - 88 * q^83 + 58 * q^84 - 20 * q^85 + 44 * q^86 - 120 * q^87 + 94 * q^88 - 72 * q^89 + 42 * q^90 + 84 * q^91 - 144 * q^92 - 36 * q^93 + 6 * q^94 + 12 * q^95 + 172 * q^96 - 60 * q^97 + 266 * q^98 - 50 * 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.k.a	$265$	$2$	265.k	53.d	$13$	$108$	$9$	$2.116$		None		✓			265.2.k.a	$2$	$0$	\(-5\)	\(-2\)	\(-9\)	\(7\)		$\mathrm{SU}(2)[C_{13}]$
265.2.k.b	$265$	$2$	265.k	53.d	$13$	$108$	$9$	$2.116$		None		✓			265.2.k.b	$2$	$0$	\(1\)	\(2\)	\(9\)	\(-11\)		$\mathrm{SU}(2)[C_{13}]$

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

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