# Properties

 Label 9295.2 Level 9295 Weight 2 Dimension 3023786 Nonzero newspaces 80 Sturm bound 13628160

## Defining parameters

 Level: $$N$$ = $$9295 = 5 \cdot 11 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$80$$ Sturm bound: $$13628160$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9295))$$.

Total New Old
Modular forms 3425280 3045874 379406
Cusp forms 3388801 3023786 365015
Eisenstein series 36479 22088 14391

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9295))$$

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
9295.2.a $$\chi_{9295}(1, \cdot)$$ 9295.2.a.a 1 1
9295.2.a.b 1
9295.2.a.c 1
9295.2.a.d 1
9295.2.a.e 1
9295.2.a.f 2
9295.2.a.g 2
9295.2.a.h 2
9295.2.a.i 2
9295.2.a.j 3
9295.2.a.k 3
9295.2.a.l 4
9295.2.a.m 4
9295.2.a.n 6
9295.2.a.o 6
9295.2.a.p 8
9295.2.a.q 8
9295.2.a.r 8
9295.2.a.s 9
9295.2.a.t 9
9295.2.a.u 9
9295.2.a.v 10
9295.2.a.w 10
9295.2.a.x 12
9295.2.a.y 12
9295.2.a.z 14
9295.2.a.ba 14
9295.2.a.bb 14
9295.2.a.bc 14
9295.2.a.bd 16
9295.2.a.be 16
9295.2.a.bf 27
9295.2.a.bg 27
9295.2.a.bh 27
9295.2.a.bi 27
9295.2.a.bj 28
9295.2.a.bk 28
9295.2.a.bl 33
9295.2.a.bm 33
9295.2.a.bn 33
9295.2.a.bo 33
9295.2.b $$\chi_{9295}(3719, \cdot)$$ n/a 776 1
9295.2.e $$\chi_{9295}(4731, \cdot)$$ n/a 516 1
9295.2.f $$\chi_{9295}(8449, \cdot)$$ n/a 768 1
9295.2.i $$\chi_{9295}(991, \cdot)$$ n/a 1024 2
9295.2.j $$\chi_{9295}(408, \cdot)$$ n/a 1540 2
9295.2.l $$\chi_{9295}(5169, \cdot)$$ n/a 1808 2
9295.2.o $$\chi_{9295}(6423, \cdot)$$ n/a 1816 2
9295.2.q $$\chi_{9295}(1858, \cdot)$$ n/a 1808 2
9295.2.s $$\chi_{9295}(1451, \cdot)$$ n/a 1232 2
9295.2.t $$\chi_{9295}(2267, \cdot)$$ n/a 1540 2
9295.2.v $$\chi_{9295}(3381, \cdot)$$ n/a 2480 4
9295.2.y $$\chi_{9295}(2344, \cdot)$$ n/a 1536 2
9295.2.z $$\chi_{9295}(3741, \cdot)$$ n/a 1024 2
9295.2.bc $$\chi_{9295}(529, \cdot)$$ n/a 1544 2
9295.2.bf $$\chi_{9295}(2534, \cdot)$$ n/a 3616 4
9295.2.bg $$\chi_{9295}(1351, \cdot)$$ n/a 2464 4
9295.2.bj $$\chi_{9295}(339, \cdot)$$ n/a 3632 4
9295.2.bl $$\chi_{9295}(1948, \cdot)$$ n/a 3080 4
9295.2.bm $$\chi_{9295}(1671, \cdot)$$ n/a 2464 4
9295.2.bo $$\chi_{9295}(868, \cdot)$$ n/a 3616 4
9295.2.bq $$\chi_{9295}(3233, \cdot)$$ n/a 3616 4
9295.2.bt $$\chi_{9295}(934, \cdot)$$ n/a 3616 4
9295.2.bv $$\chi_{9295}(188, \cdot)$$ n/a 3080 4
9295.2.bw $$\chi_{9295}(716, \cdot)$$ n/a 7248 12
9295.2.bx $$\chi_{9295}(146, \cdot)$$ n/a 4928 8
9295.2.bz $$\chi_{9295}(268, \cdot)$$ n/a 7232 8
9295.2.ca $$\chi_{9295}(1591, \cdot)$$ n/a 4928 8
9295.2.cc $$\chi_{9295}(337, \cdot)$$ n/a 7232 8
9295.2.ce $$\chi_{9295}(508, \cdot)$$ n/a 7264 8
9295.2.ch $$\chi_{9295}(239, \cdot)$$ n/a 7232 8
9295.2.cj $$\chi_{9295}(2127, \cdot)$$ n/a 7232 8
9295.2.cm $$\chi_{9295}(584, \cdot)$$ n/a 10944 12
9295.2.cn $$\chi_{9295}(441, \cdot)$$ n/a 7248 12
9295.2.cq $$\chi_{9295}(144, \cdot)$$ n/a 10896 12
9295.2.cr $$\chi_{9295}(1329, \cdot)$$ n/a 7232 8
9295.2.cu $$\chi_{9295}(361, \cdot)$$ n/a 4928 8
9295.2.cv $$\chi_{9295}(654, \cdot)$$ n/a 7232 8
9295.2.cy $$\chi_{9295}(276, \cdot)$$ n/a 14592 24
9295.2.da $$\chi_{9295}(122, \cdot)$$ n/a 21840 24
9295.2.db $$\chi_{9295}(21, \cdot)$$ n/a 17472 24
9295.2.dd $$\chi_{9295}(142, \cdot)$$ n/a 26112 24
9295.2.df $$\chi_{9295}(417, \cdot)$$ n/a 26112 24
9295.2.di $$\chi_{9295}(109, \cdot)$$ n/a 26112 24
9295.2.dk $$\chi_{9295}(177, \cdot)$$ n/a 21840 24
9295.2.dl $$\chi_{9295}(427, \cdot)$$ n/a 14464 16
9295.2.dn $$\chi_{9295}(19, \cdot)$$ n/a 14464 16
9295.2.dq $$\chi_{9295}(822, \cdot)$$ n/a 14464 16
9295.2.ds $$\chi_{9295}(992, \cdot)$$ n/a 14464 16
9295.2.du $$\chi_{9295}(596, \cdot)$$ n/a 9856 16
9295.2.dv $$\chi_{9295}(258, \cdot)$$ n/a 14464 16
9295.2.dx $$\chi_{9295}(196, \cdot)$$ n/a 34944 48
9295.2.dy $$\chi_{9295}(419, \cdot)$$ n/a 21792 24
9295.2.eb $$\chi_{9295}(56, \cdot)$$ n/a 14592 24
9295.2.ec $$\chi_{9295}(199, \cdot)$$ n/a 21888 24
9295.2.ef $$\chi_{9295}(14, \cdot)$$ n/a 52224 48
9295.2.ei $$\chi_{9295}(181, \cdot)$$ n/a 34944 48
9295.2.ej $$\chi_{9295}(64, \cdot)$$ n/a 52224 48
9295.2.em $$\chi_{9295}(232, \cdot)$$ n/a 43680 48
9295.2.eo $$\chi_{9295}(54, \cdot)$$ n/a 52224 48
9295.2.er $$\chi_{9295}(87, \cdot)$$ n/a 52224 48
9295.2.et $$\chi_{9295}(43, \cdot)$$ n/a 52224 48
9295.2.ev $$\chi_{9295}(76, \cdot)$$ n/a 34944 48
9295.2.ew $$\chi_{9295}(67, \cdot)$$ n/a 43680 48
9295.2.ey $$\chi_{9295}(16, \cdot)$$ n/a 69888 96
9295.2.ez $$\chi_{9295}(47, \cdot)$$ n/a 104448 96
9295.2.fb $$\chi_{9295}(294, \cdot)$$ n/a 104448 96
9295.2.fe $$\chi_{9295}(118, \cdot)$$ n/a 104448 96
9295.2.fg $$\chi_{9295}(233, \cdot)$$ n/a 104448 96
9295.2.fi $$\chi_{9295}(96, \cdot)$$ n/a 69888 96
9295.2.fj $$\chi_{9295}(203, \cdot)$$ n/a 104448 96
9295.2.fn $$\chi_{9295}(4, \cdot)$$ n/a 104448 96
9295.2.fo $$\chi_{9295}(36, \cdot)$$ n/a 69888 96
9295.2.fr $$\chi_{9295}(9, \cdot)$$ n/a 104448 96
9295.2.ft $$\chi_{9295}(97, \cdot)$$ n/a 208896 192
9295.2.fu $$\chi_{9295}(6, \cdot)$$ n/a 139776 192
9295.2.fw $$\chi_{9295}(17, \cdot)$$ n/a 208896 192
9295.2.fy $$\chi_{9295}(68, \cdot)$$ n/a 208896 192
9295.2.gb $$\chi_{9295}(24, \cdot)$$ n/a 208896 192
9295.2.gd $$\chi_{9295}(37, \cdot)$$ n/a 208896 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9295))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9295)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(715))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1859))$$$$^{\oplus 2}$$