Space of modular forms of level 2156 and weight 2

• Label: 2156.2
• Level: 2156
• Weight: 2
• Dimension: 76805
• Nonzero newspaces: 32
• Sturm bound: 564480
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(564480\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2156))\).

	Total	New	Old
Modular forms	144120	78553	65567
Cusp forms	138121	76805	61316
Eisenstein series	5999	1748	4251

Trace form

76805 * q - 125 * q^2 - 4 * q^3 - 125 * q^4 - 262 * q^5 - 113 * q^6 - 8 * q^7 - 209 * q^8 - 252 * q^9 - 84 * q^10 + q^11 - 220 * q^12 - 215 * q^13 - 120 * q^14 + 24 * q^15 - 57 * q^16 - 257 * q^17 - 76 * q^18 + 19 * q^19 - 88 * q^20 - 266 * q^21 - 242 * q^22 - 7 * q^23 - 131 * q^24 - 208 * q^25 - 136 * q^26 - 40 * q^27 - 192 * q^28 - 399 * q^29 - 132 * q^30 + 28 * q^31 - 120 * q^32 - 260 * q^33 - 288 * q^34 + 30 * q^35 - 186 * q^36 - 112 * q^37 - 66 * q^38 + 95 * q^39 - 100 * q^40 - 79 * q^41 - 114 * q^42 + 42 * q^43 - 133 * q^44 - 252 * q^45 - 90 * q^46 + 115 * q^47 - 210 * q^48 - 140 * q^49 - 363 * q^50 + 161 * q^51 - 118 * q^52 - 181 * q^53 - 180 * q^54 + 79 * q^55 - 300 * q^56 - 427 * q^57 - 102 * q^58 + 68 * q^59 - 116 * q^60 - 141 * q^61 - 38 * q^62 + 126 * q^63 - 101 * q^64 - 2 * q^65 - 81 * q^66 + 163 * q^67 - 48 * q^68 + 133 * q^69 - 126 * q^70 + 260 * q^71 - 123 * q^72 + 73 * q^73 - 116 * q^74 + 459 * q^75 - 168 * q^76 - 207 * q^77 - 602 * q^78 + 237 * q^79 - 350 * q^80 + 181 * q^81 - 305 * q^82 + 83 * q^83 - 600 * q^84 - 267 * q^85 - 529 * q^86 - 62 * q^87 - 409 * q^88 - 473 * q^89 - 956 * q^90 - 94 * q^91 - 510 * q^92 - 528 * q^93 - 636 * q^94 - 289 * q^95 - 918 * q^96 - 568 * q^97 - 756 * q^98 - 134 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2156))\)

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
2156.2.a	\(\chi_{2156}(1, \cdot)\)	2156.2.a.a	1	1
		2156.2.a.b	1
		2156.2.a.c	2
		2156.2.a.d	2
		2156.2.a.e	2
		2156.2.a.f	2
		2156.2.a.g	3
		2156.2.a.h	3
		2156.2.a.i	3
		2156.2.a.j	3
		2156.2.a.k	3
		2156.2.a.l	4
		2156.2.a.m	4
2156.2.c	\(\chi_{2156}(1077, \cdot)\)	2156.2.c.a	8	1
		2156.2.c.b	16
		2156.2.c.c	16
2156.2.d	\(\chi_{2156}(1275, \cdot)\)	n/a	236	1
2156.2.f	\(\chi_{2156}(1959, \cdot)\)	n/a	200	1
2156.2.i	\(\chi_{2156}(177, \cdot)\)	2156.2.i.a	2	2
		2156.2.i.b	2
		2156.2.i.c	2
		2156.2.i.d	2
		2156.2.i.e	4
		2156.2.i.f	4
		2156.2.i.g	4
		2156.2.i.h	4
		2156.2.i.i	4
		2156.2.i.j	6
		2156.2.i.k	6
		2156.2.i.l	6
		2156.2.i.m	6
		2156.2.i.n	8
		2156.2.i.o	8
2156.2.j	\(\chi_{2156}(785, \cdot)\)	n/a	164	4
2156.2.l	\(\chi_{2156}(815, \cdot)\)	n/a	400	2
2156.2.n	\(\chi_{2156}(263, \cdot)\)	n/a	464	2
2156.2.q	\(\chi_{2156}(901, \cdot)\)	2156.2.q.a	8	2
		2156.2.q.b	8
		2156.2.q.c	16
		2156.2.q.d	16
		2156.2.q.e	32
2156.2.r	\(\chi_{2156}(309, \cdot)\)	n/a	288	6
2156.2.u	\(\chi_{2156}(587, \cdot)\)	n/a	928	4
2156.2.w	\(\chi_{2156}(491, \cdot)\)	n/a	944	4
2156.2.x	\(\chi_{2156}(293, \cdot)\)	n/a	160	4
2156.2.bb	\(\chi_{2156}(111, \cdot)\)	n/a	1680	6
2156.2.bd	\(\chi_{2156}(43, \cdot)\)	n/a	1992	6
2156.2.be	\(\chi_{2156}(153, \cdot)\)	n/a	336	6
2156.2.bg	\(\chi_{2156}(361, \cdot)\)	n/a	320	8
2156.2.bh	\(\chi_{2156}(221, \cdot)\)	n/a	552	12
2156.2.bi	\(\chi_{2156}(117, \cdot)\)	n/a	320	8
2156.2.bl	\(\chi_{2156}(79, \cdot)\)	n/a	1856	8
2156.2.bn	\(\chi_{2156}(31, \cdot)\)	n/a	1856	8
2156.2.bp	\(\chi_{2156}(113, \cdot)\)	n/a	1344	24
2156.2.bq	\(\chi_{2156}(241, \cdot)\)	n/a	672	12
2156.2.bt	\(\chi_{2156}(219, \cdot)\)	n/a	3984	12
2156.2.bv	\(\chi_{2156}(199, \cdot)\)	n/a	3360	12
2156.2.by	\(\chi_{2156}(13, \cdot)\)	n/a	1344	24
2156.2.bz	\(\chi_{2156}(127, \cdot)\)	n/a	7968	24
2156.2.cb	\(\chi_{2156}(27, \cdot)\)	n/a	7968	24
2156.2.ce	\(\chi_{2156}(9, \cdot)\)	n/a	2688	48
2156.2.cg	\(\chi_{2156}(3, \cdot)\)	n/a	15936	48
2156.2.ci	\(\chi_{2156}(39, \cdot)\)	n/a	15936	48
2156.2.cl	\(\chi_{2156}(17, \cdot)\)	n/a	2688	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2156))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2156)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2156))\)\(^{\oplus 1}\)