# Properties

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

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## 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

 $$125336 q - 266 q^{2} - 200 q^{3} - 264 q^{4} - 332 q^{5} - 260 q^{6} - 198 q^{7} - 260 q^{8} - 66 q^{9} + O(q^{10})$$ $$125336 q - 266 q^{2} - 200 q^{3} - 264 q^{4} - 332 q^{5} - 260 q^{6} - 198 q^{7} - 260 q^{8} - 66 q^{9} - 264 q^{10} - 196 q^{11} - 268 q^{12} - 360 q^{13} - 508 q^{14} - 194 q^{15} - 272 q^{16} - 598 q^{17} - 262 q^{18} - 192 q^{19} - 260 q^{20} - 326 q^{21} - 264 q^{22} - 198 q^{23} - 264 q^{24} - 54 q^{25} - 288 q^{26} - 386 q^{27} - 256 q^{28} - 324 q^{29} - 268 q^{30} - 214 q^{31} - 256 q^{32} - 598 q^{33} - 260 q^{34} - 202 q^{35} - 268 q^{36} - 324 q^{37} - 276 q^{38} - 204 q^{39} - 512 q^{40} - 18 q^{41} - 264 q^{42} - 92 q^{43} - 268 q^{44} - 208 q^{45} - 252 q^{46} - 110 q^{47} - 256 q^{48} - 492 q^{49} - 270 q^{50} - 62 q^{51} - 288 q^{52} - 544 q^{53} - 264 q^{54} - 54 q^{55} - 272 q^{56} + 30 q^{57} - 276 q^{58} - 132 q^{59} - 264 q^{60} - 228 q^{61} - 248 q^{62} - 98 q^{63} - 264 q^{64} - 624 q^{65} - 500 q^{66} - 184 q^{67} - 264 q^{68} - 342 q^{69} - 256 q^{70} - 198 q^{71} - 260 q^{72} - 66 q^{73} - 264 q^{74} - 228 q^{75} - 252 q^{76} - 314 q^{77} - 288 q^{78} - 378 q^{79} - 256 q^{80} - 548 q^{81} - 264 q^{82} - 200 q^{83} - 608 q^{84} - 374 q^{85} - 456 q^{86} - 270 q^{87} - 496 q^{88} - 258 q^{89} - 892 q^{90} - 264 q^{91} - 816 q^{92} - 698 q^{93} - 664 q^{94} - 330 q^{95} - 1144 q^{96} - 790 q^{97} - 702 q^{98} - 392 q^{99} + O(q^{100})$$

## 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

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