# Properties

 Label 2695.2 Level 2695 Weight 2 Dimension 241510 Nonzero newspaces 48 Sturm bound 1128960 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$2695 = 5 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$1128960$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2695))$$.

Total New Old
Modular forms 287040 246750 40290
Cusp forms 277441 241510 35931
Eisenstein series 9599 5240 4359

## Trace form

 $$241510 q - 256 q^{2} - 250 q^{3} - 232 q^{4} - 365 q^{5} - 692 q^{6} - 272 q^{7} - 380 q^{8} - 176 q^{9} + O(q^{10})$$ $$241510 q - 256 q^{2} - 250 q^{3} - 232 q^{4} - 365 q^{5} - 692 q^{6} - 272 q^{7} - 380 q^{8} - 176 q^{9} - 306 q^{10} - 806 q^{11} - 376 q^{12} - 180 q^{13} - 216 q^{14} - 579 q^{15} - 528 q^{16} - 136 q^{17} + 20 q^{18} - 124 q^{19} - 198 q^{20} - 764 q^{21} - 352 q^{22} - 410 q^{23} + 4 q^{24} - 303 q^{25} - 528 q^{26} - 118 q^{27} - 200 q^{28} - 356 q^{29} - 346 q^{30} - 638 q^{31} - 84 q^{32} - 188 q^{33} - 420 q^{34} - 426 q^{35} - 1248 q^{36} - 242 q^{37} - 164 q^{38} - 264 q^{39} - 592 q^{40} - 696 q^{41} - 444 q^{42} - 440 q^{43} - 328 q^{44} - 910 q^{45} - 892 q^{46} - 192 q^{47} - 448 q^{48} - 440 q^{49} - 1078 q^{50} - 628 q^{51} - 484 q^{52} - 68 q^{53} - 276 q^{54} - 467 q^{55} - 2136 q^{56} - 300 q^{57} - 444 q^{58} - 234 q^{59} - 858 q^{60} - 996 q^{61} - 408 q^{62} - 420 q^{63} - 972 q^{64} - 532 q^{65} - 1498 q^{66} - 730 q^{67} - 692 q^{68} - 590 q^{69} - 726 q^{70} - 1474 q^{71} - 1100 q^{72} - 444 q^{73} - 368 q^{74} - 753 q^{75} - 1560 q^{76} - 414 q^{77} - 1700 q^{78} - 368 q^{79} - 870 q^{80} - 1402 q^{81} - 688 q^{82} - 488 q^{83} - 1496 q^{84} - 786 q^{85} - 1348 q^{86} - 836 q^{87} - 950 q^{88} - 730 q^{89} - 1434 q^{90} - 1096 q^{91} - 896 q^{92} - 1070 q^{93} - 620 q^{94} - 692 q^{95} - 2260 q^{96} - 314 q^{97} - 1176 q^{98} - 878 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2695))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2695.2.a $$\chi_{2695}(1, \cdot)$$ 2695.2.a.a 1 1
2695.2.a.b 1
2695.2.a.c 1
2695.2.a.d 2
2695.2.a.e 2
2695.2.a.f 2
2695.2.a.g 3
2695.2.a.h 3
2695.2.a.i 3
2695.2.a.j 4
2695.2.a.k 4
2695.2.a.l 4
2695.2.a.m 5
2695.2.a.n 5
2695.2.a.o 5
2695.2.a.p 5
2695.2.a.q 6
2695.2.a.r 6
2695.2.a.s 8
2695.2.a.t 8
2695.2.a.u 10
2695.2.a.v 10
2695.2.a.w 10
2695.2.a.x 10
2695.2.a.y 10
2695.2.a.z 10
2695.2.b $$\chi_{2695}(1079, \cdot)$$ n/a 204 1
2695.2.c $$\chi_{2695}(1616, \cdot)$$ n/a 160 1
2695.2.h $$\chi_{2695}(2694, \cdot)$$ n/a 232 1
2695.2.i $$\chi_{2695}(606, \cdot)$$ n/a 264 2
2695.2.j $$\chi_{2695}(342, \cdot)$$ n/a 400 2
2695.2.k $$\chi_{2695}(197, \cdot)$$ n/a 472 2
2695.2.n $$\chi_{2695}(246, \cdot)$$ n/a 656 4
2695.2.o $$\chi_{2695}(1979, \cdot)$$ n/a 464 2
2695.2.t $$\chi_{2695}(1684, \cdot)$$ n/a 400 2
2695.2.u $$\chi_{2695}(901, \cdot)$$ n/a 320 2
2695.2.v $$\chi_{2695}(386, \cdot)$$ n/a 1104 6
2695.2.w $$\chi_{2695}(244, \cdot)$$ n/a 928 4
2695.2.bb $$\chi_{2695}(391, \cdot)$$ n/a 640 4
2695.2.bc $$\chi_{2695}(344, \cdot)$$ n/a 944 4
2695.2.bd $$\chi_{2695}(263, \cdot)$$ n/a 928 4
2695.2.be $$\chi_{2695}(1783, \cdot)$$ n/a 800 4
2695.2.bh $$\chi_{2695}(384, \cdot)$$ n/a 1992 6
2695.2.bm $$\chi_{2695}(76, \cdot)$$ n/a 1344 6
2695.2.bn $$\chi_{2695}(309, \cdot)$$ n/a 1680 6
2695.2.bo $$\chi_{2695}(361, \cdot)$$ n/a 1280 8
2695.2.br $$\chi_{2695}(393, \cdot)$$ n/a 1888 8
2695.2.bs $$\chi_{2695}(48, \cdot)$$ n/a 1856 8
2695.2.bt $$\chi_{2695}(221, \cdot)$$ n/a 2256 12
2695.2.bw $$\chi_{2695}(43, \cdot)$$ n/a 3984 12
2695.2.bx $$\chi_{2695}(188, \cdot)$$ n/a 3360 12
2695.2.by $$\chi_{2695}(656, \cdot)$$ n/a 1280 8
2695.2.bz $$\chi_{2695}(214, \cdot)$$ n/a 1856 8
2695.2.ce $$\chi_{2695}(19, \cdot)$$ n/a 1856 8
2695.2.cf $$\chi_{2695}(36, \cdot)$$ n/a 5376 24
2695.2.cg $$\chi_{2695}(131, \cdot)$$ n/a 2688 12
2695.2.ch $$\chi_{2695}(144, \cdot)$$ n/a 3360 12
2695.2.cm $$\chi_{2695}(54, \cdot)$$ n/a 3984 12
2695.2.cp $$\chi_{2695}(313, \cdot)$$ n/a 3712 16
2695.2.cq $$\chi_{2695}(18, \cdot)$$ n/a 3712 16
2695.2.cr $$\chi_{2695}(64, \cdot)$$ n/a 7968 24
2695.2.cs $$\chi_{2695}(6, \cdot)$$ n/a 5376 24
2695.2.cx $$\chi_{2695}(139, \cdot)$$ n/a 7968 24
2695.2.da $$\chi_{2695}(12, \cdot)$$ n/a 6720 24
2695.2.db $$\chi_{2695}(32, \cdot)$$ n/a 7968 24
2695.2.dc $$\chi_{2695}(16, \cdot)$$ n/a 10752 48
2695.2.dd $$\chi_{2695}(27, \cdot)$$ n/a 15936 48
2695.2.de $$\chi_{2695}(8, \cdot)$$ n/a 15936 48
2695.2.dh $$\chi_{2695}(24, \cdot)$$ n/a 15936 48
2695.2.dm $$\chi_{2695}(4, \cdot)$$ n/a 15936 48
2695.2.dn $$\chi_{2695}(61, \cdot)$$ n/a 10752 48
2695.2.do $$\chi_{2695}(2, \cdot)$$ n/a 31872 96
2695.2.dp $$\chi_{2695}(3, \cdot)$$ n/a 31872 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2695))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2695)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 2}$$