Space of modular forms of level 3136 and weight 2

• Label: 3136.2
• Level: 3136
• Weight: 2
• Dimension: 161437
• Nonzero newspaces: 32
• Sturm bound: 1204224
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 3136 = 2^{6} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(1204224\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3136))\).

	Total	New	Old
Modular forms	305376	163571	141805
Cusp forms	296737	161437	135300
Eisenstein series	8639	2134	6505

Trace form

161437 * q - 248 * q^2 - 186 * q^3 - 248 * q^4 - 248 * q^5 - 248 * q^6 - 216 * q^7 - 440 * q^8 - 313 * q^9 - 248 * q^10 - 190 * q^11 - 248 * q^12 - 256 * q^13 - 288 * q^14 - 336 * q^15 - 248 * q^16 - 442 * q^17 - 248 * q^18 - 194 * q^19 - 248 * q^20 - 288 * q^21 - 432 * q^22 - 188 * q^23 - 208 * q^24 - 299 * q^25 - 208 * q^26 - 180 * q^27 - 288 * q^28 - 424 * q^29 - 168 * q^30 - 164 * q^31 - 208 * q^32 - 160 * q^33 - 208 * q^34 - 216 * q^35 - 360 * q^36 - 240 * q^37 - 208 * q^38 - 188 * q^39 - 208 * q^40 - 310 * q^41 - 288 * q^42 - 342 * q^43 - 240 * q^44 - 252 * q^45 - 248 * q^46 - 204 * q^47 - 248 * q^48 - 504 * q^49 - 800 * q^50 - 160 * q^51 - 296 * q^52 - 272 * q^53 - 312 * q^54 - 100 * q^55 - 288 * q^56 - 556 * q^57 - 320 * q^58 - 118 * q^59 - 344 * q^60 - 256 * q^61 - 280 * q^62 - 216 * q^63 - 536 * q^64 - 684 * q^65 - 328 * q^66 - 98 * q^67 - 296 * q^68 - 260 * q^69 - 288 * q^70 - 268 * q^71 - 320 * q^72 - 310 * q^73 - 304 * q^74 - 130 * q^75 - 312 * q^76 - 288 * q^77 - 464 * q^78 - 156 * q^79 - 208 * q^80 - 359 * q^81 - 168 * q^82 - 186 * q^83 - 288 * q^84 - 432 * q^85 - 144 * q^86 - 188 * q^87 - 168 * q^88 - 262 * q^89 - 104 * q^90 - 132 * q^91 - 288 * q^92 - 112 * q^93 - 152 * q^94 - 24 * q^95 - 112 * q^96 + 46 * q^97 - 288 * q^98 - 318 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3136))\)

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
3136.2.a	\(\chi_{3136}(1, \cdot)\)	3136.2.a.a	1	1
		3136.2.a.b	1
		3136.2.a.c	1
		3136.2.a.d	1
		3136.2.a.e	1
		3136.2.a.f	1
		3136.2.a.g	1
		3136.2.a.h	1
		3136.2.a.i	1
		3136.2.a.j	1
		3136.2.a.k	1
		3136.2.a.l	1
		3136.2.a.m	1
		3136.2.a.n	1
		3136.2.a.o	1
		3136.2.a.p	1
		3136.2.a.q	1
		3136.2.a.r	1
		3136.2.a.s	1
		3136.2.a.t	1
		3136.2.a.u	1
		3136.2.a.v	1
		3136.2.a.w	1
		3136.2.a.x	1
		3136.2.a.y	1
		3136.2.a.z	1
		3136.2.a.ba	1
		3136.2.a.bb	1
		3136.2.a.bc	1
		3136.2.a.bd	2
		3136.2.a.be	2
		3136.2.a.bf	2
		3136.2.a.bg	2
		3136.2.a.bh	2
		3136.2.a.bi	2
		3136.2.a.bj	2
		3136.2.a.bk	2
		3136.2.a.bl	2
		3136.2.a.bm	2
		3136.2.a.bn	2
		3136.2.a.bo	2
		3136.2.a.bp	2
		3136.2.a.bq	2
		3136.2.a.br	2
		3136.2.a.bs	2
		3136.2.a.bt	2
		3136.2.a.bu	2
		3136.2.a.bv	2
		3136.2.a.bw	2
		3136.2.a.bx	2
		3136.2.a.by	2
		3136.2.a.bz	4
3136.2.b	\(\chi_{3136}(1569, \cdot)\)	3136.2.b.a	2	1
		3136.2.b.b	2
		3136.2.b.c	2
		3136.2.b.d	4
		3136.2.b.e	4
		3136.2.b.f	4
		3136.2.b.g	4
		3136.2.b.h	4
		3136.2.b.i	4
		3136.2.b.j	4
		3136.2.b.k	8
		3136.2.b.l	12
		3136.2.b.m	12
		3136.2.b.n	16
3136.2.e	\(\chi_{3136}(1567, \cdot)\)	3136.2.e.a	8	1
		3136.2.e.b	8
		3136.2.e.c	8
		3136.2.e.d	12
		3136.2.e.e	12
		3136.2.e.f	32
3136.2.f	\(\chi_{3136}(3135, \cdot)\)	3136.2.f.a	2	1
		3136.2.f.b	2
		3136.2.f.c	4
		3136.2.f.d	4
		3136.2.f.e	4
		3136.2.f.f	4
		3136.2.f.g	8
		3136.2.f.h	8
		3136.2.f.i	8
		3136.2.f.j	16
		3136.2.f.k	16
3136.2.i	\(\chi_{3136}(961, \cdot)\)	n/a	152	2
3136.2.j	\(\chi_{3136}(783, \cdot)\)	n/a	152	2
3136.2.m	\(\chi_{3136}(785, \cdot)\)	n/a	154	2
3136.2.p	\(\chi_{3136}(1599, \cdot)\)	n/a	152	2
3136.2.q	\(\chi_{3136}(31, \cdot)\)	n/a	160	2
3136.2.t	\(\chi_{3136}(2529, \cdot)\)	n/a	160	2
3136.2.u	\(\chi_{3136}(449, \cdot)\)	n/a	660	6
3136.2.v	\(\chi_{3136}(393, \cdot)\)	None	0	4
3136.2.y	\(\chi_{3136}(391, \cdot)\)	None	0	4
3136.2.ba	\(\chi_{3136}(815, \cdot)\)	n/a	304	4
3136.2.bb	\(\chi_{3136}(177, \cdot)\)	n/a	304	4
3136.2.bf	\(\chi_{3136}(447, \cdot)\)	n/a	660	6
3136.2.bg	\(\chi_{3136}(223, \cdot)\)	n/a	672	6
3136.2.bj	\(\chi_{3136}(225, \cdot)\)	n/a	672	6
3136.2.bk	\(\chi_{3136}(197, \cdot)\)	n/a	2584	8
3136.2.bl	\(\chi_{3136}(195, \cdot)\)	n/a	2528	8
3136.2.bo	\(\chi_{3136}(65, \cdot)\)	n/a	1320	12
3136.2.bq	\(\chi_{3136}(361, \cdot)\)	None	0	8
3136.2.br	\(\chi_{3136}(215, \cdot)\)	None	0	8
3136.2.bt	\(\chi_{3136}(113, \cdot)\)	n/a	1320	12
3136.2.bw	\(\chi_{3136}(111, \cdot)\)	n/a	1320	12
3136.2.bx	\(\chi_{3136}(289, \cdot)\)	n/a	1344	12
3136.2.ca	\(\chi_{3136}(159, \cdot)\)	n/a	1344	12
3136.2.cb	\(\chi_{3136}(255, \cdot)\)	n/a	1320	12
3136.2.cg	\(\chi_{3136}(19, \cdot)\)	n/a	5056	16
3136.2.ch	\(\chi_{3136}(165, \cdot)\)	n/a	5056	16
3136.2.ci	\(\chi_{3136}(55, \cdot)\)	None	0	24
3136.2.cl	\(\chi_{3136}(57, \cdot)\)	None	0	24
3136.2.cn	\(\chi_{3136}(81, \cdot)\)	n/a	2640	24
3136.2.co	\(\chi_{3136}(47, \cdot)\)	n/a	2640	24
3136.2.cq	\(\chi_{3136}(27, \cdot)\)	n/a	21408	48
3136.2.cr	\(\chi_{3136}(29, \cdot)\)	n/a	21408	48
3136.2.cv	\(\chi_{3136}(87, \cdot)\)	None	0	48
3136.2.cw	\(\chi_{3136}(9, \cdot)\)	None	0	48
3136.2.da	\(\chi_{3136}(37, \cdot)\)	n/a	42816	96
3136.2.db	\(\chi_{3136}(3, \cdot)\)	n/a	42816	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3136))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3136)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 2}\)