Space of modular forms of level 3312 and weight 2

• Label: 3312.2
• Level: 3312
• Weight: 2
• Dimension: 134069
• Nonzero newspaces: 32
• Sturm bound: 1216512
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(1216512\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3312))\).

	Total	New	Old
Modular forms	309056	135769	173287
Cusp forms	299201	134069	165132
Eisenstein series	9855	1700	8155

Trace form

134069 * q - 120 * q^2 - 120 * q^3 - 124 * q^4 - 155 * q^5 - 160 * q^6 - 101 * q^7 - 132 * q^8 - 48 * q^9 - 364 * q^10 - 117 * q^11 - 160 * q^12 - 167 * q^13 - 84 * q^14 - 126 * q^15 - 76 * q^16 - 253 * q^17 - 120 * q^18 - 277 * q^19 - 20 * q^20 - 174 * q^21 - 28 * q^22 - 74 * q^23 - 272 * q^24 + 23 * q^25 - 4 * q^26 - 84 * q^27 - 284 * q^28 - 91 * q^29 - 120 * q^30 - 65 * q^31 - 60 * q^32 - 318 * q^33 - 100 * q^34 + 57 * q^35 - 152 * q^36 - 467 * q^37 - 212 * q^38 - 6 * q^39 - 236 * q^40 - 3 * q^41 - 240 * q^42 + 27 * q^43 - 292 * q^44 - 154 * q^45 - 440 * q^46 - 48 * q^47 - 264 * q^48 - 337 * q^49 - 288 * q^50 - 56 * q^51 - 244 * q^52 - 133 * q^53 - 248 * q^54 - 141 * q^55 - 324 * q^56 - 84 * q^57 - 196 * q^58 - 41 * q^59 - 376 * q^60 - 103 * q^61 - 324 * q^62 - 126 * q^63 - 220 * q^64 - 459 * q^65 - 400 * q^66 - 113 * q^67 - 292 * q^68 - 285 * q^69 - 176 * q^70 - 227 * q^71 - 384 * q^72 - 59 * q^73 - 236 * q^74 - 224 * q^75 - 52 * q^76 - 283 * q^77 - 376 * q^78 - 247 * q^79 - 388 * q^80 - 512 * q^81 - 380 * q^82 - 363 * q^83 - 448 * q^84 - 221 * q^85 - 412 * q^86 - 258 * q^87 - 268 * q^88 - 157 * q^89 - 448 * q^90 - 558 * q^91 - 224 * q^92 - 338 * q^93 - 316 * q^94 - 431 * q^95 - 296 * q^96 - 335 * q^97 - 304 * q^98 - 150 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3312))\)

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
3312.2.a	\(\chi_{3312}(1, \cdot)\)	3312.2.a.a	1	1
		3312.2.a.b	1
		3312.2.a.c	1
		3312.2.a.d	1
		3312.2.a.e	1
		3312.2.a.f	1
		3312.2.a.g	1
		3312.2.a.h	1
		3312.2.a.i	1
		3312.2.a.j	1
		3312.2.a.k	1
		3312.2.a.l	1
		3312.2.a.m	1
		3312.2.a.n	1
		3312.2.a.o	1
		3312.2.a.p	1
		3312.2.a.q	1
		3312.2.a.r	1
		3312.2.a.s	2
		3312.2.a.t	2
		3312.2.a.u	2
		3312.2.a.v	2
		3312.2.a.w	2
		3312.2.a.x	2
		3312.2.a.y	2
		3312.2.a.z	2
		3312.2.a.ba	2
		3312.2.a.bb	2
		3312.2.a.bc	2
		3312.2.a.bd	2
		3312.2.a.be	2
		3312.2.a.bf	3
		3312.2.a.bg	4
		3312.2.a.bh	4
3312.2.b	\(\chi_{3312}(1241, \cdot)\)	None	0	1
3312.2.e	\(\chi_{3312}(1151, \cdot)\)	3312.2.e.a	2	1
		3312.2.e.b	2
		3312.2.e.c	2
		3312.2.e.d	2
		3312.2.e.e	2
		3312.2.e.f	2
		3312.2.e.g	16
		3312.2.e.h	16
3312.2.f	\(\chi_{3312}(1657, \cdot)\)	None	0	1
3312.2.i	\(\chi_{3312}(2575, \cdot)\)	3312.2.i.a	4	1
		3312.2.i.b	8
		3312.2.i.c	8
		3312.2.i.d	8
		3312.2.i.e	8
		3312.2.i.f	8
		3312.2.i.g	16
3312.2.j	\(\chi_{3312}(2807, \cdot)\)	None	0	1
3312.2.m	\(\chi_{3312}(2897, \cdot)\)	3312.2.m.a	8	1
		3312.2.m.b	8
		3312.2.m.c	8
		3312.2.m.d	24
3312.2.n	\(\chi_{3312}(919, \cdot)\)	None	0	1
3312.2.q	\(\chi_{3312}(1105, \cdot)\)	n/a	264	2
3312.2.r	\(\chi_{3312}(91, \cdot)\)	n/a	476	2
3312.2.u	\(\chi_{3312}(829, \cdot)\)	n/a	440	2
3312.2.v	\(\chi_{3312}(323, \cdot)\)	n/a	352	2
3312.2.y	\(\chi_{3312}(413, \cdot)\)	n/a	384	2
3312.2.bb	\(\chi_{3312}(2023, \cdot)\)	None	0	2
3312.2.bc	\(\chi_{3312}(689, \cdot)\)	n/a	284	2
3312.2.bf	\(\chi_{3312}(599, \cdot)\)	None	0	2
3312.2.bg	\(\chi_{3312}(367, \cdot)\)	n/a	288	2
3312.2.bj	\(\chi_{3312}(553, \cdot)\)	None	0	2
3312.2.bk	\(\chi_{3312}(47, \cdot)\)	n/a	264	2
3312.2.bn	\(\chi_{3312}(137, \cdot)\)	None	0	2
3312.2.bo	\(\chi_{3312}(289, \cdot)\)	n/a	590	10
3312.2.bq	\(\chi_{3312}(875, \cdot)\)	n/a	2112	4
3312.2.br	\(\chi_{3312}(965, \cdot)\)	n/a	2288	4
3312.2.bu	\(\chi_{3312}(643, \cdot)\)	n/a	2288	4
3312.2.bv	\(\chi_{3312}(277, \cdot)\)	n/a	2112	4
3312.2.bz	\(\chi_{3312}(199, \cdot)\)	None	0	10
3312.2.ca	\(\chi_{3312}(17, \cdot)\)	n/a	480	10
3312.2.cd	\(\chi_{3312}(71, \cdot)\)	None	0	10
3312.2.ce	\(\chi_{3312}(559, \cdot)\)	n/a	600	10
3312.2.ch	\(\chi_{3312}(73, \cdot)\)	None	0	10
3312.2.ci	\(\chi_{3312}(719, \cdot)\)	n/a	480	10
3312.2.cl	\(\chi_{3312}(89, \cdot)\)	None	0	10
3312.2.cm	\(\chi_{3312}(49, \cdot)\)	n/a	2840	20
3312.2.cn	\(\chi_{3312}(53, \cdot)\)	n/a	3840	20
3312.2.cq	\(\chi_{3312}(35, \cdot)\)	n/a	3840	20
3312.2.cr	\(\chi_{3312}(325, \cdot)\)	n/a	4760	20
3312.2.cu	\(\chi_{3312}(19, \cdot)\)	n/a	4760	20
3312.2.cv	\(\chi_{3312}(281, \cdot)\)	None	0	20
3312.2.cy	\(\chi_{3312}(95, \cdot)\)	n/a	2880	20
3312.2.cz	\(\chi_{3312}(25, \cdot)\)	None	0	20
3312.2.dc	\(\chi_{3312}(79, \cdot)\)	n/a	2880	20
3312.2.dd	\(\chi_{3312}(119, \cdot)\)	None	0	20
3312.2.dg	\(\chi_{3312}(65, \cdot)\)	n/a	2840	20
3312.2.dh	\(\chi_{3312}(7, \cdot)\)	None	0	20
3312.2.dl	\(\chi_{3312}(13, \cdot)\)	n/a	22880	40
3312.2.dm	\(\chi_{3312}(43, \cdot)\)	n/a	22880	40
3312.2.dp	\(\chi_{3312}(5, \cdot)\)	n/a	22880	40
3312.2.dq	\(\chi_{3312}(59, \cdot)\)	n/a	22880	40

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3312))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1656))\)\(^{\oplus 2}\)