Properties

Label 9196.2
Level 9196
Weight 2
Dimension 1486397
Nonzero newspaces 48
Sturm bound 10454400

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Defining parameters

Level: \( N \) = \( 9196 = 2^{2} \cdot 11^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(10454400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9196))\).

Total New Old
Modular forms 2628000 1495953 1132047
Cusp forms 2599201 1486397 1112804
Eisenstein series 28799 9556 19243

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9196))\)

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
9196.2.a \(\chi_{9196}(1, \cdot)\) 9196.2.a.a 1 1
9196.2.a.b 1
9196.2.a.c 1
9196.2.a.d 1
9196.2.a.e 1
9196.2.a.f 1
9196.2.a.g 1
9196.2.a.h 2
9196.2.a.i 6
9196.2.a.j 6
9196.2.a.k 6
9196.2.a.l 6
9196.2.a.m 6
9196.2.a.n 6
9196.2.a.o 7
9196.2.a.p 7
9196.2.a.q 8
9196.2.a.r 8
9196.2.a.s 10
9196.2.a.t 10
9196.2.a.u 14
9196.2.a.v 14
9196.2.a.w 20
9196.2.a.x 20
9196.2.b \(\chi_{9196}(4597, \cdot)\) n/a 180 1
9196.2.d \(\chi_{9196}(7259, \cdot)\) n/a 972 1
9196.2.g \(\chi_{9196}(6535, \cdot)\) n/a 1072 1
9196.2.i \(\chi_{9196}(3389, \cdot)\) n/a 362 2
9196.2.j \(\chi_{9196}(2205, \cdot)\) n/a 648 4
9196.2.k \(\chi_{9196}(3147, \cdot)\) n/a 2144 2
9196.2.o \(\chi_{9196}(1209, \cdot)\) n/a 360 2
9196.2.q \(\chi_{9196}(1451, \cdot)\) n/a 2128 2
9196.2.r \(\chi_{9196}(1453, \cdot)\) n/a 1092 6
9196.2.t \(\chi_{9196}(1291, \cdot)\) n/a 4256 4
9196.2.w \(\chi_{9196}(723, \cdot)\) n/a 3888 4
9196.2.y \(\chi_{9196}(645, \cdot)\) n/a 720 4
9196.2.z \(\chi_{9196}(837, \cdot)\) n/a 1980 10
9196.2.ba \(\chi_{9196}(729, \cdot)\) n/a 1440 8
9196.2.bd \(\chi_{9196}(967, \cdot)\) n/a 6384 6
9196.2.be \(\chi_{9196}(243, \cdot)\) n/a 6432 6
9196.2.bg \(\chi_{9196}(241, \cdot)\) n/a 1080 6
9196.2.bj \(\chi_{9196}(571, \cdot)\) n/a 11880 10
9196.2.bl \(\chi_{9196}(417, \cdot)\) n/a 2200 10
9196.2.bn \(\chi_{9196}(683, \cdot)\) n/a 13160 10
9196.2.bp \(\chi_{9196}(239, \cdot)\) n/a 8512 8
9196.2.br \(\chi_{9196}(1129, \cdot)\) n/a 1440 8
9196.2.bv \(\chi_{9196}(27, \cdot)\) n/a 8512 8
9196.2.bw \(\chi_{9196}(45, \cdot)\) n/a 4400 20
9196.2.bx \(\chi_{9196}(9, \cdot)\) n/a 4320 24
9196.2.by \(\chi_{9196}(229, \cdot)\) n/a 7920 40
9196.2.cb \(\chi_{9196}(331, \cdot)\) n/a 26320 20
9196.2.cc \(\chi_{9196}(87, \cdot)\) n/a 26320 20
9196.2.ce \(\chi_{9196}(65, \cdot)\) n/a 4400 20
9196.2.ch \(\chi_{9196}(717, \cdot)\) n/a 4320 24
9196.2.cj \(\chi_{9196}(3, \cdot)\) n/a 25536 24
9196.2.ck \(\chi_{9196}(215, \cdot)\) n/a 25536 24
9196.2.cn \(\chi_{9196}(177, \cdot)\) n/a 13200 60
9196.2.cp \(\chi_{9196}(75, \cdot)\) n/a 52640 40
9196.2.cr \(\chi_{9196}(189, \cdot)\) n/a 8800 40
9196.2.ct \(\chi_{9196}(39, \cdot)\) n/a 47520 40
9196.2.cv \(\chi_{9196}(49, \cdot)\) n/a 17600 80
9196.2.cx \(\chi_{9196}(67, \cdot)\) n/a 78960 60
9196.2.cz \(\chi_{9196}(21, \cdot)\) n/a 13200 60
9196.2.db \(\chi_{9196}(43, \cdot)\) n/a 78960 60
9196.2.de \(\chi_{9196}(145, \cdot)\) n/a 17600 80
9196.2.dg \(\chi_{9196}(7, \cdot)\) n/a 105280 80
9196.2.dh \(\chi_{9196}(31, \cdot)\) n/a 105280 80
9196.2.dk \(\chi_{9196}(5, \cdot)\) n/a 52800 240
9196.2.dm \(\chi_{9196}(35, \cdot)\) n/a 315840 240
9196.2.do \(\chi_{9196}(13, \cdot)\) n/a 52800 240
9196.2.dq \(\chi_{9196}(15, \cdot)\) n/a 315840 240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9196))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9196)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(836))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2299))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4598))\)\(^{\oplus 2}\)