Space of modular forms of level 2704 and weight 2

• Label: 2704.2
• Level: 2704
• Weight: 2
• Dimension: 125336
• Nonzero newspaces: 28
• Sturm bound: 908544
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 2704 = 2^{4} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(908544\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2704))\).

	Total	New	Old
Modular forms	230328	127177	103151
Cusp forms	223945	125336	98609
Eisenstein series	6383	1841	4542

Trace form

125336 * q - 266 * q^2 - 200 * q^3 - 264 * q^4 - 332 * q^5 - 260 * q^6 - 198 * q^7 - 260 * q^8 - 66 * q^9 - 264 * q^10 - 196 * q^11 - 268 * q^12 - 360 * q^13 - 508 * q^14 - 194 * q^15 - 272 * q^16 - 598 * q^17 - 262 * q^18 - 192 * q^19 - 260 * q^20 - 326 * q^21 - 264 * q^22 - 198 * q^23 - 264 * q^24 - 54 * q^25 - 288 * q^26 - 386 * q^27 - 256 * q^28 - 324 * q^29 - 268 * q^30 - 214 * q^31 - 256 * q^32 - 598 * q^33 - 260 * q^34 - 202 * q^35 - 268 * q^36 - 324 * q^37 - 276 * q^38 - 204 * q^39 - 512 * q^40 - 18 * q^41 - 264 * q^42 - 92 * q^43 - 268 * q^44 - 208 * q^45 - 252 * q^46 - 110 * q^47 - 256 * q^48 - 492 * q^49 - 270 * q^50 - 62 * q^51 - 288 * q^52 - 544 * q^53 - 264 * q^54 - 54 * q^55 - 272 * q^56 + 30 * q^57 - 276 * q^58 - 132 * q^59 - 264 * q^60 - 228 * q^61 - 248 * q^62 - 98 * q^63 - 264 * q^64 - 624 * q^65 - 500 * q^66 - 184 * q^67 - 264 * q^68 - 342 * q^69 - 256 * q^70 - 198 * q^71 - 260 * q^72 - 66 * q^73 - 264 * q^74 - 228 * q^75 - 252 * q^76 - 314 * q^77 - 288 * q^78 - 378 * q^79 - 256 * q^80 - 548 * q^81 - 264 * q^82 - 200 * q^83 - 608 * q^84 - 374 * q^85 - 456 * q^86 - 270 * q^87 - 496 * q^88 - 258 * q^89 - 892 * q^90 - 264 * q^91 - 816 * q^92 - 698 * q^93 - 664 * q^94 - 330 * q^95 - 1144 * q^96 - 790 * q^97 - 702 * q^98 - 392 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2704))\)

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
2704.2.a	\(\chi_{2704}(1, \cdot)\)	2704.2.a.a	1	1
		2704.2.a.b	1
		2704.2.a.c	1
		2704.2.a.d	1
		2704.2.a.e	1
		2704.2.a.f	1
		2704.2.a.g	1
		2704.2.a.h	1
		2704.2.a.i	1
		2704.2.a.j	1
		2704.2.a.k	1
		2704.2.a.l	1
		2704.2.a.m	1
		2704.2.a.n	1
		2704.2.a.o	2
		2704.2.a.p	2
		2704.2.a.q	2
		2704.2.a.r	2
		2704.2.a.s	2
		2704.2.a.t	2
		2704.2.a.u	2
		2704.2.a.v	3
		2704.2.a.w	3
		2704.2.a.x	3
		2704.2.a.y	3
		2704.2.a.z	3
		2704.2.a.ba	3
		2704.2.a.bb	3
		2704.2.a.bc	3
		2704.2.a.bd	4
		2704.2.a.be	4
		2704.2.a.bf	6
		2704.2.a.bg	6
2704.2.b	\(\chi_{2704}(1353, \cdot)\)	None	0	1
2704.2.e	\(\chi_{2704}(1689, \cdot)\)	None	0	1
2704.2.f	\(\chi_{2704}(337, \cdot)\)	2704.2.f.a	2	1
		2704.2.f.b	2
		2704.2.f.c	2
		2704.2.f.d	2
		2704.2.f.e	2
		2704.2.f.f	2
		2704.2.f.g	2
		2704.2.f.h	2
		2704.2.f.i	2
		2704.2.f.j	2
		2704.2.f.k	4
		2704.2.f.l	4
		2704.2.f.m	6
		2704.2.f.n	6
		2704.2.f.o	6
		2704.2.f.p	6
		2704.2.f.q	8
		2704.2.f.r	12
2704.2.i	\(\chi_{2704}(529, \cdot)\)	n/a	144	2
2704.2.k	\(\chi_{2704}(239, \cdot)\)	n/a	154	2
2704.2.l	\(\chi_{2704}(915, \cdot)\)	n/a	596	2
2704.2.n	\(\chi_{2704}(677, \cdot)\)	n/a	598	2
2704.2.p	\(\chi_{2704}(1013, \cdot)\)	n/a	596	2
2704.2.s	\(\chi_{2704}(99, \cdot)\)	n/a	596	2
2704.2.u	\(\chi_{2704}(775, \cdot)\)	None	0	2
2704.2.w	\(\chi_{2704}(1713, \cdot)\)	n/a	144	2
2704.2.z	\(\chi_{2704}(1881, \cdot)\)	None	0	2
2704.2.ba	\(\chi_{2704}(361, \cdot)\)	None	0	2
2704.2.bc	\(\chi_{2704}(695, \cdot)\)	None	0	4
2704.2.bf	\(\chi_{2704}(19, \cdot)\)	n/a	1192	4
2704.2.bh	\(\chi_{2704}(485, \cdot)\)	n/a	1192	4
2704.2.bj	\(\chi_{2704}(653, \cdot)\)	n/a	1192	4
2704.2.bk	\(\chi_{2704}(587, \cdot)\)	n/a	1192	4
2704.2.bm	\(\chi_{2704}(319, \cdot)\)	n/a	308	4
2704.2.bo	\(\chi_{2704}(209, \cdot)\)	n/a	1080	12
2704.2.br	\(\chi_{2704}(129, \cdot)\)	n/a	1080	12
2704.2.bs	\(\chi_{2704}(25, \cdot)\)	None	0	12
2704.2.bv	\(\chi_{2704}(105, \cdot)\)	None	0	12
2704.2.bw	\(\chi_{2704}(81, \cdot)\)	n/a	2160	24
2704.2.by	\(\chi_{2704}(135, \cdot)\)	None	0	24
2704.2.bz	\(\chi_{2704}(187, \cdot)\)	n/a	8688	24
2704.2.cb	\(\chi_{2704}(77, \cdot)\)	n/a	8688	24
2704.2.cd	\(\chi_{2704}(53, \cdot)\)	n/a	8688	24
2704.2.cg	\(\chi_{2704}(83, \cdot)\)	n/a	8688	24
2704.2.ci	\(\chi_{2704}(31, \cdot)\)	n/a	2184	24
2704.2.ck	\(\chi_{2704}(121, \cdot)\)	None	0	24
2704.2.cl	\(\chi_{2704}(9, \cdot)\)	None	0	24
2704.2.co	\(\chi_{2704}(17, \cdot)\)	n/a	2160	24
2704.2.cq	\(\chi_{2704}(15, \cdot)\)	n/a	4368	48
2704.2.ct	\(\chi_{2704}(115, \cdot)\)	n/a	17376	48
2704.2.cv	\(\chi_{2704}(29, \cdot)\)	n/a	17376	48
2704.2.cx	\(\chi_{2704}(69, \cdot)\)	n/a	17376	48
2704.2.cy	\(\chi_{2704}(11, \cdot)\)	n/a	17376	48
2704.2.da	\(\chi_{2704}(7, \cdot)\)	None	0	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2704))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2704)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)\(^{\oplus 2}\)