Space of modular forms of level 1656 and weight 2

• Label: 1656.2
• Level: 1656
• Weight: 2
• Dimension: 33352
• Nonzero newspaces: 24
• Sturm bound: 304128
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(304128\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1656))\).

	Total	New	Old
Modular forms	78144	34108	44036
Cusp forms	73921	33352	40569
Eisenstein series	4223	756	3467

Trace form

33352 * q - 62 * q^2 - 82 * q^3 - 62 * q^4 - 8 * q^5 - 72 * q^6 - 62 * q^7 - 38 * q^8 - 158 * q^9 - 150 * q^10 - 32 * q^11 - 60 * q^12 + 4 * q^13 - 38 * q^14 - 40 * q^15 - 46 * q^16 - 92 * q^17 - 88 * q^18 - 154 * q^19 - 86 * q^20 + 24 * q^21 - 94 * q^22 - 48 * q^23 - 224 * q^24 - 116 * q^25 - 122 * q^26 - 88 * q^27 - 214 * q^28 - 12 * q^29 - 180 * q^30 - 34 * q^31 - 142 * q^32 - 162 * q^33 - 38 * q^34 - 160 * q^35 - 188 * q^36 - 56 * q^37 - 142 * q^38 - 160 * q^39 - 86 * q^40 - 144 * q^41 - 188 * q^42 - 160 * q^43 - 150 * q^44 - 4 * q^45 - 214 * q^46 - 260 * q^47 - 128 * q^48 - 94 * q^49 - 122 * q^50 - 106 * q^51 - 14 * q^52 + 6 * q^53 - 64 * q^54 - 210 * q^55 - 2 * q^56 - 118 * q^57 - 46 * q^58 - 90 * q^59 + 44 * q^60 + 16 * q^61 + 62 * q^62 - 152 * q^63 - 158 * q^64 - 64 * q^65 + 120 * q^66 - 16 * q^67 + 102 * q^68 - 22 * q^69 - 40 * q^70 - 82 * q^71 + 116 * q^72 - 348 * q^73 + 176 * q^74 - 186 * q^75 + 112 * q^76 - 24 * q^77 + 60 * q^78 + 8 * q^79 + 324 * q^80 - 198 * q^81 - 106 * q^82 - 64 * q^83 + 40 * q^84 + 50 * q^85 + 254 * q^86 - 124 * q^87 + 82 * q^88 - 110 * q^89 - 60 * q^90 - 92 * q^91 + 78 * q^92 + 20 * q^93 + 84 * q^94 - 62 * q^95 - 184 * q^96 - 168 * q^97 - 82 * q^98 - 148 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1656))\)

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
1656.2.a	\(\chi_{1656}(1, \cdot)\)	1656.2.a.a	1	1
		1656.2.a.b	1
		1656.2.a.c	1
		1656.2.a.d	1
		1656.2.a.e	1
		1656.2.a.f	1
		1656.2.a.g	1
		1656.2.a.h	1
		1656.2.a.i	1
		1656.2.a.j	2
		1656.2.a.k	2
		1656.2.a.l	2
		1656.2.a.m	2
		1656.2.a.n	3
		1656.2.a.o	4
		1656.2.a.p	4
1656.2.b	\(\chi_{1656}(413, \cdot)\)	1656.2.b.a	8	1
		1656.2.b.b	8
		1656.2.b.c	80
1656.2.e	\(\chi_{1656}(1151, \cdot)\)	None	0	1
1656.2.f	\(\chi_{1656}(829, \cdot)\)	n/a	110	1
1656.2.i	\(\chi_{1656}(919, \cdot)\)	None	0	1
1656.2.j	\(\chi_{1656}(323, \cdot)\)	1656.2.j.a	44	1
		1656.2.j.b	44
1656.2.m	\(\chi_{1656}(1241, \cdot)\)	1656.2.m.a	24	1
1656.2.n	\(\chi_{1656}(91, \cdot)\)	n/a	118	1
1656.2.q	\(\chi_{1656}(553, \cdot)\)	n/a	132	2
1656.2.t	\(\chi_{1656}(643, \cdot)\)	n/a	568	2
1656.2.u	\(\chi_{1656}(137, \cdot)\)	n/a	144	2
1656.2.x	\(\chi_{1656}(875, \cdot)\)	n/a	528	2
1656.2.y	\(\chi_{1656}(367, \cdot)\)	None	0	2
1656.2.bb	\(\chi_{1656}(277, \cdot)\)	n/a	528	2
1656.2.bc	\(\chi_{1656}(47, \cdot)\)	None	0	2
1656.2.bf	\(\chi_{1656}(965, \cdot)\)	n/a	568	2
1656.2.bg	\(\chi_{1656}(73, \cdot)\)	n/a	300	10
1656.2.bj	\(\chi_{1656}(19, \cdot)\)	n/a	1180	10
1656.2.bk	\(\chi_{1656}(17, \cdot)\)	n/a	240	10
1656.2.bn	\(\chi_{1656}(35, \cdot)\)	n/a	960	10
1656.2.bo	\(\chi_{1656}(199, \cdot)\)	None	0	10
1656.2.br	\(\chi_{1656}(325, \cdot)\)	n/a	1180	10
1656.2.bs	\(\chi_{1656}(71, \cdot)\)	None	0	10
1656.2.bv	\(\chi_{1656}(53, \cdot)\)	n/a	960	10
1656.2.bw	\(\chi_{1656}(25, \cdot)\)	n/a	1440	20
1656.2.bx	\(\chi_{1656}(5, \cdot)\)	n/a	5680	20
1656.2.ca	\(\chi_{1656}(95, \cdot)\)	None	0	20
1656.2.cb	\(\chi_{1656}(13, \cdot)\)	n/a	5680	20
1656.2.ce	\(\chi_{1656}(7, \cdot)\)	None	0	20
1656.2.cf	\(\chi_{1656}(59, \cdot)\)	n/a	5680	20
1656.2.ci	\(\chi_{1656}(65, \cdot)\)	n/a	1440	20
1656.2.cj	\(\chi_{1656}(43, \cdot)\)	n/a	5680	20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1656))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1656)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)\(^{\oplus 2}\)