Space of modular forms of level 465 and weight 2

• Label: 465.2
• Level: 465
• Weight: 2
• Dimension: 5099
• Nonzero newspaces: 24
• Newform subspaces: 61
• Sturm bound: 30720
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 61 \)
Sturm bound:			\(30720\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(465))\).

	Total	New	Old
Modular forms	8160	5443	2717
Cusp forms	7201	5099	2102
Eisenstein series	959	344	615

Trace form

5099 * q + 5 * q^2 - 27 * q^3 - 51 * q^4 - q^5 - 89 * q^6 - 52 * q^7 + 9 * q^8 - 31 * q^9 - 85 * q^10 + 20 * q^11 - 25 * q^12 - 42 * q^13 + 24 * q^14 - 42 * q^15 - 147 * q^16 + 14 * q^17 - 25 * q^18 - 48 * q^19 + 9 * q^20 - 92 * q^21 - 152 * q^22 - 36 * q^23 - 129 * q^24 - 111 * q^25 - 82 * q^26 - 27 * q^27 - 324 * q^28 - 86 * q^29 - 119 * q^30 - 269 * q^31 - 287 * q^32 - 86 * q^33 - 242 * q^34 - 52 * q^35 - 121 * q^36 - 182 * q^37 - 52 * q^38 - 90 * q^39 - 201 * q^40 - 38 * q^41 - 66 * q^42 - 44 * q^43 + 76 * q^44 - 46 * q^45 - 108 * q^46 + 32 * q^47 - 91 * q^48 - 109 * q^49 - 145 * q^50 - 248 * q^51 - 266 * q^52 - 46 * q^53 - 359 * q^54 - 190 * q^55 - 420 * q^56 - 182 * q^57 - 394 * q^58 - 52 * q^59 - 235 * q^60 - 534 * q^61 - 267 * q^62 - 292 * q^63 - 427 * q^64 - 162 * q^65 - 496 * q^66 - 136 * q^67 - 290 * q^68 - 186 * q^69 - 336 * q^70 - 152 * q^71 - 351 * q^72 - 126 * q^73 - 206 * q^74 - 117 * q^75 - 332 * q^76 - 24 * q^77 + 106 * q^78 + 20 * q^79 + 33 * q^80 + 29 * q^81 + 86 * q^82 + 60 * q^83 + 386 * q^84 - 76 * q^85 + 140 * q^86 + 116 * q^87 + 144 * q^88 + 102 * q^89 + 140 * q^90 - 68 * q^91 + 168 * q^92 + 241 * q^93 + 40 * q^94 + 12 * q^95 + 233 * q^96 + 34 * q^97 + 157 * q^98 + 140 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)

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
465.2.a	\(\chi_{465}(1, \cdot)\)	465.2.a.a	1	1
		465.2.a.b	1
		465.2.a.c	2
		465.2.a.d	2
		465.2.a.e	3
		465.2.a.f	3
		465.2.a.g	3
		465.2.a.h	4
465.2.c	\(\chi_{465}(94, \cdot)\)	465.2.c.a	10	1
		465.2.c.b	22
465.2.e	\(\chi_{465}(371, \cdot)\)	465.2.e.a	44	1
465.2.g	\(\chi_{465}(464, \cdot)\)	465.2.g.a	4	1
		465.2.g.b	4
		465.2.g.c	4
		465.2.g.d	8
		465.2.g.e	8
		465.2.g.f	32
465.2.i	\(\chi_{465}(211, \cdot)\)	465.2.i.a	2	2
		465.2.i.b	4
		465.2.i.c	6
		465.2.i.d	8
		465.2.i.e	10
		465.2.i.f	14
465.2.j	\(\chi_{465}(247, \cdot)\)	465.2.j.a	64	2
465.2.k	\(\chi_{465}(32, \cdot)\)	465.2.k.a	60	2
		465.2.k.b	60
465.2.n	\(\chi_{465}(16, \cdot)\)	465.2.n.a	4	4
		465.2.n.b	4
		465.2.n.c	8
		465.2.n.d	16
		465.2.n.e	20
		465.2.n.f	28
465.2.o	\(\chi_{465}(26, \cdot)\)	465.2.o.a	84	2
465.2.q	\(\chi_{465}(304, \cdot)\)	465.2.q.a	4	2
		465.2.q.b	60
465.2.t	\(\chi_{465}(119, \cdot)\)	465.2.t.a	4	2
		465.2.t.b	4
		465.2.t.c	8
		465.2.t.d	104
465.2.w	\(\chi_{465}(29, \cdot)\)	465.2.w.a	8	4
		465.2.w.b	8
		465.2.w.c	224
465.2.y	\(\chi_{465}(116, \cdot)\)	465.2.y.a	176	4
465.2.ba	\(\chi_{465}(4, \cdot)\)	465.2.ba.a	128	4
465.2.be	\(\chi_{465}(98, \cdot)\)	465.2.be.a	240	4
465.2.bf	\(\chi_{465}(37, \cdot)\)	465.2.bf.a	128	4
465.2.bg	\(\chi_{465}(76, \cdot)\)	465.2.bg.a	32	8
		465.2.bg.b	40
		465.2.bg.c	48
		465.2.bg.d	56
465.2.bj	\(\chi_{465}(2, \cdot)\)	465.2.bj.a	480	8
465.2.bk	\(\chi_{465}(58, \cdot)\)	465.2.bk.a	256	8
465.2.bm	\(\chi_{465}(44, \cdot)\)	465.2.bm.a	8	8
		465.2.bm.b	8
		465.2.bm.c	8
		465.2.bm.d	8
		465.2.bm.e	448
465.2.bp	\(\chi_{465}(19, \cdot)\)	465.2.bp.a	256	8
465.2.br	\(\chi_{465}(11, \cdot)\)	465.2.br.a	336	8
465.2.bs	\(\chi_{465}(13, \cdot)\)	465.2.bs.a	512	16
465.2.bt	\(\chi_{465}(38, \cdot)\)	465.2.bt.a	960	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(465))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(465)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)