Space of modular forms of level 265 and weight 2

• Label: 265.2
• Level: 265
• Weight: 2
• Dimension: 2417
• Nonzero newspaces: 12
• Newform subspaces: 24
• Sturm bound: 11232
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 265 = 5 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 24 \)
Sturm bound:			\(11232\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(265))\).

	Total	New	Old
Modular forms	3016	2725	291
Cusp forms	2601	2417	184
Eisenstein series	415	308	107

Trace form

2417 * q - 55 * q^2 - 56 * q^3 - 59 * q^4 - 79 * q^5 - 168 * q^6 - 60 * q^7 - 67 * q^8 - 65 * q^9 - 81 * q^10 - 168 * q^11 - 80 * q^12 - 66 * q^13 - 76 * q^14 - 82 * q^15 - 187 * q^16 - 70 * q^17 - 91 * q^18 - 72 * q^19 - 85 * q^20 - 188 * q^21 - 88 * q^22 - 76 * q^23 - 112 * q^24 - 79 * q^25 - 198 * q^26 - 92 * q^27 - 108 * q^28 - 82 * q^29 - 90 * q^30 - 188 * q^31 - 115 * q^32 - 100 * q^33 - 106 * q^34 - 86 * q^35 - 247 * q^36 - 90 * q^37 - 112 * q^38 - 108 * q^39 - 54 * q^40 - 146 * q^41 + 60 * q^42 + 8 * q^43 + 72 * q^44 + 39 * q^45 - 124 * q^46 - 48 * q^47 + 344 * q^48 - 5 * q^49 + 36 * q^50 - 20 * q^51 + 214 * q^52 + 51 * q^53 + 88 * q^54 - 12 * q^55 + 36 * q^56 + 76 * q^57 + 92 * q^58 - 8 * q^59 + 154 * q^60 - 166 * q^61 - 44 * q^62 + 104 * q^63 + 29 * q^64 - 40 * q^65 - 92 * q^66 - 68 * q^67 - 100 * q^68 - 148 * q^69 - 102 * q^70 - 228 * q^71 - 247 * q^72 - 126 * q^73 - 166 * q^74 - 82 * q^75 - 296 * q^76 - 148 * q^77 - 220 * q^78 - 132 * q^79 - 109 * q^80 - 277 * q^81 - 178 * q^82 - 136 * q^83 - 276 * q^84 - 96 * q^85 - 288 * q^86 - 68 * q^87 + 28 * q^88 - 12 * q^89 + 91 * q^90 - 60 * q^91 + 248 * q^92 + 28 * q^93 + 428 * q^94 + 6 * q^95 + 112 * q^96 + 292 * q^97 + 193 * q^98 + 312 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(265))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
265.2.a	\(\chi_{265}(1, \cdot)\)	265.2.a.a	1	1
		265.2.a.b	2
		265.2.a.c	2
		265.2.a.d	2
		265.2.a.e	2
		265.2.a.f	2
		265.2.a.g	2
		265.2.a.h	4
265.2.b	\(\chi_{265}(54, \cdot)\)	265.2.b.a	26	1
265.2.c	\(\chi_{265}(211, \cdot)\)	265.2.c.a	18	1
265.2.d	\(\chi_{265}(264, \cdot)\)	265.2.d.a	4	1
		265.2.d.b	4
		265.2.d.c	16
265.2.e	\(\chi_{265}(23, \cdot)\)	265.2.e.a	2	2
		265.2.e.b	48
265.2.j	\(\chi_{265}(83, \cdot)\)	265.2.j.a	2	2
		265.2.j.b	48
265.2.k	\(\chi_{265}(16, \cdot)\)	265.2.k.a	108	12
		265.2.k.b	108
265.2.l	\(\chi_{265}(4, \cdot)\)	265.2.l.a	288	12
265.2.m	\(\chi_{265}(6, \cdot)\)	265.2.m.a	216	12
265.2.n	\(\chi_{265}(24, \cdot)\)	265.2.n.a	312	12
265.2.o	\(\chi_{265}(3, \cdot)\)	265.2.o.a	600	24
265.2.t	\(\chi_{265}(2, \cdot)\)	265.2.t.a	600	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(265))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(265)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)