Space of modular forms of level 1904 and weight 2

• Label: 1904.2
• Level: 1904
• Weight: 2
• Dimension: 58526
• Nonzero newspaces: 52
• Sturm bound: 442368
• Trace bound: 61

Defining parameters

Level:	\( N \)	=	\( 1904 = 2^{4} \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 52 \)
Sturm bound:			\(442368\)
Trace bound:			\(61\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1904))\).

	Total	New	Old
Modular forms	113280	59878	53402
Cusp forms	107905	58526	49379
Eisenstein series	5375	1352	4023

Trace form

58526 * q - 112 * q^2 - 86 * q^3 - 104 * q^4 - 138 * q^5 - 88 * q^6 - 102 * q^7 - 256 * q^8 - 26 * q^9 - 104 * q^10 - 70 * q^11 - 120 * q^12 - 132 * q^13 - 144 * q^14 - 188 * q^15 - 136 * q^16 - 269 * q^17 - 224 * q^18 - 42 * q^19 - 88 * q^20 - 138 * q^21 - 272 * q^22 - 42 * q^23 - 104 * q^24 + 22 * q^25 - 88 * q^26 - 68 * q^27 - 120 * q^28 - 292 * q^29 - 120 * q^30 - 94 * q^31 - 72 * q^32 - 186 * q^33 - 108 * q^34 - 194 * q^35 - 288 * q^36 - 82 * q^37 - 152 * q^38 - 84 * q^39 - 136 * q^40 - 20 * q^41 - 280 * q^42 - 176 * q^43 - 216 * q^44 - 200 * q^45 - 176 * q^46 - 50 * q^47 - 312 * q^48 - 362 * q^49 - 464 * q^50 - 109 * q^51 - 464 * q^52 - 234 * q^53 - 440 * q^54 - 60 * q^55 - 320 * q^56 - 132 * q^57 - 320 * q^58 - 54 * q^59 - 440 * q^60 - 170 * q^61 - 256 * q^62 - 10 * q^63 - 440 * q^64 - 156 * q^65 - 328 * q^66 - 62 * q^67 - 176 * q^68 - 124 * q^69 - 216 * q^70 - 48 * q^71 - 280 * q^72 + 150 * q^73 - 104 * q^74 + 312 * q^75 - 56 * q^76 - 2 * q^77 - 288 * q^78 + 102 * q^79 - 72 * q^80 + 48 * q^81 - 104 * q^82 + 112 * q^83 - 152 * q^84 - 282 * q^85 - 232 * q^86 + 12 * q^87 - 72 * q^88 + 70 * q^89 + 24 * q^90 - 220 * q^91 - 344 * q^92 + 6 * q^93 - 24 * q^94 - 198 * q^95 + 72 * q^96 - 196 * q^97 - 8 * q^98 - 488 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1904))\)

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
1904.2.a	\(\chi_{1904}(1, \cdot)\)	1904.2.a.a	1	1
		1904.2.a.b	1
		1904.2.a.c	1
		1904.2.a.d	1
		1904.2.a.e	1
		1904.2.a.f	2
		1904.2.a.g	2
		1904.2.a.h	2
		1904.2.a.i	2
		1904.2.a.j	2
		1904.2.a.k	2
		1904.2.a.l	2
		1904.2.a.m	3
		1904.2.a.n	3
		1904.2.a.o	3
		1904.2.a.p	3
		1904.2.a.q	4
		1904.2.a.r	4
		1904.2.a.s	4
		1904.2.a.t	5
1904.2.b	\(\chi_{1904}(953, \cdot)\)	None	0	1
1904.2.c	\(\chi_{1904}(1121, \cdot)\)	1904.2.c.a	2	1
		1904.2.c.b	2
		1904.2.c.c	4
		1904.2.c.d	4
		1904.2.c.e	6
		1904.2.c.f	8
		1904.2.c.g	8
		1904.2.c.h	10
		1904.2.c.i	10
1904.2.h	\(\chi_{1904}(1903, \cdot)\)	1904.2.h.a	8	1
		1904.2.h.b	16
		1904.2.h.c	48
1904.2.i	\(\chi_{1904}(1735, \cdot)\)	None	0	1
1904.2.j	\(\chi_{1904}(783, \cdot)\)	1904.2.j.a	8	1
		1904.2.j.b	24
		1904.2.j.c	32
1904.2.k	\(\chi_{1904}(951, \cdot)\)	None	0	1
1904.2.p	\(\chi_{1904}(169, \cdot)\)	None	0	1
1904.2.q	\(\chi_{1904}(1089, \cdot)\)	n/a	128	2
1904.2.s	\(\chi_{1904}(1203, \cdot)\)	n/a	568	2
1904.2.t	\(\chi_{1904}(1373, \cdot)\)	n/a	432	2
1904.2.w	\(\chi_{1904}(1177, \cdot)\)	None	0	2
1904.2.x	\(\chi_{1904}(1007, \cdot)\)	n/a	144	2
1904.2.z	\(\chi_{1904}(475, \cdot)\)	n/a	568	2
1904.2.bc	\(\chi_{1904}(307, \cdot)\)	n/a	512	2
1904.2.be	\(\chi_{1904}(477, \cdot)\)	n/a	384	2
1904.2.bf	\(\chi_{1904}(645, \cdot)\)	n/a	432	2
1904.2.bi	\(\chi_{1904}(225, \cdot)\)	n/a	108	2
1904.2.bj	\(\chi_{1904}(55, \cdot)\)	None	0	2
1904.2.bm	\(\chi_{1904}(421, \cdot)\)	n/a	432	2
1904.2.bn	\(\chi_{1904}(251, \cdot)\)	n/a	568	2
1904.2.bp	\(\chi_{1904}(1257, \cdot)\)	None	0	2
1904.2.bu	\(\chi_{1904}(1055, \cdot)\)	n/a	128	2
1904.2.bv	\(\chi_{1904}(1223, \cdot)\)	None	0	2
1904.2.bw	\(\chi_{1904}(271, \cdot)\)	n/a	144	2
1904.2.bx	\(\chi_{1904}(103, \cdot)\)	None	0	2
1904.2.cc	\(\chi_{1904}(137, \cdot)\)	None	0	2
1904.2.cd	\(\chi_{1904}(305, \cdot)\)	n/a	140	2
1904.2.ce	\(\chi_{1904}(1063, \cdot)\)	None	0	4
1904.2.cg	\(\chi_{1904}(1233, \cdot)\)	n/a	216	4
1904.2.ci	\(\chi_{1904}(83, \cdot)\)	n/a	1136	4
1904.2.ck	\(\chi_{1904}(253, \cdot)\)	n/a	864	4
1904.2.cm	\(\chi_{1904}(195, \cdot)\)	n/a	1136	4
1904.2.co	\(\chi_{1904}(365, \cdot)\)	n/a	864	4
1904.2.cq	\(\chi_{1904}(111, \cdot)\)	n/a	288	4
1904.2.cs	\(\chi_{1904}(281, \cdot)\)	None	0	4
1904.2.cv	\(\chi_{1904}(523, \cdot)\)	n/a	1136	4
1904.2.cw	\(\chi_{1904}(149, \cdot)\)	n/a	1136	4
1904.2.cy	\(\chi_{1904}(361, \cdot)\)	None	0	4
1904.2.db	\(\chi_{1904}(47, \cdot)\)	n/a	288	4
1904.2.dc	\(\chi_{1904}(171, \cdot)\)	n/a	1024	4
1904.2.df	\(\chi_{1904}(339, \cdot)\)	n/a	1136	4
1904.2.dh	\(\chi_{1904}(373, \cdot)\)	n/a	1136	4
1904.2.di	\(\chi_{1904}(205, \cdot)\)	n/a	1024	4
1904.2.dk	\(\chi_{1904}(81, \cdot)\)	n/a	280	4
1904.2.dn	\(\chi_{1904}(327, \cdot)\)	None	0	4
1904.2.dp	\(\chi_{1904}(557, \cdot)\)	n/a	1136	4
1904.2.dq	\(\chi_{1904}(115, \cdot)\)	n/a	1136	4
1904.2.dt	\(\chi_{1904}(99, \cdot)\)	n/a	1728	8
1904.2.dv	\(\chi_{1904}(125, \cdot)\)	n/a	2272	8
1904.2.dw	\(\chi_{1904}(71, \cdot)\)	None	0	8
1904.2.dz	\(\chi_{1904}(351, \cdot)\)	n/a	432	8
1904.2.ea	\(\chi_{1904}(97, \cdot)\)	n/a	560	8
1904.2.ed	\(\chi_{1904}(41, \cdot)\)	None	0	8
1904.2.ef	\(\chi_{1904}(211, \cdot)\)	n/a	1728	8
1904.2.eh	\(\chi_{1904}(181, \cdot)\)	n/a	2272	8
1904.2.ej	\(\chi_{1904}(417, \cdot)\)	n/a	560	8
1904.2.el	\(\chi_{1904}(87, \cdot)\)	None	0	8
1904.2.en	\(\chi_{1904}(53, \cdot)\)	n/a	2272	8
1904.2.ep	\(\chi_{1904}(451, \cdot)\)	n/a	2272	8
1904.2.er	\(\chi_{1904}(485, \cdot)\)	n/a	2272	8
1904.2.et	\(\chi_{1904}(19, \cdot)\)	n/a	2272	8
1904.2.ev	\(\chi_{1904}(9, \cdot)\)	None	0	8
1904.2.ex	\(\chi_{1904}(383, \cdot)\)	n/a	576	8
1904.2.ey	\(\chi_{1904}(5, \cdot)\)	n/a	4544	16
1904.2.fa	\(\chi_{1904}(11, \cdot)\)	n/a	4544	16
1904.2.fd	\(\chi_{1904}(73, \cdot)\)	None	0	16
1904.2.fe	\(\chi_{1904}(129, \cdot)\)	n/a	1120	16
1904.2.fh	\(\chi_{1904}(79, \cdot)\)	n/a	1152	16
1904.2.fi	\(\chi_{1904}(23, \cdot)\)	None	0	16
1904.2.fk	\(\chi_{1904}(173, \cdot)\)	n/a	4544	16
1904.2.fm	\(\chi_{1904}(107, \cdot)\)	n/a	4544	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1904))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1904)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(952))\)\(^{\oplus 2}\)