Properties

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

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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

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