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Properties

Label 7436.2
Level 7436
Weight 2
Dimension 961947
Nonzero newspaces 48
Sturm bound 6814080

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Defining parameters

Level: \( N \) = \( 7436 = 2^{2} \cdot 11 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(6814080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7436))\).

Total New Old
Modular forms 1714920 969311 745609
Cusp forms 1692121 961947 730174
Eisenstein series 22799 7364 15435

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7436))\)

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
7436.2.a \(\chi_{7436}(1, \cdot)\) 7436.2.a.a 1 1
7436.2.a.b 1
7436.2.a.c 1
7436.2.a.d 1
7436.2.a.e 2
7436.2.a.f 2
7436.2.a.g 2
7436.2.a.h 2
7436.2.a.i 2
7436.2.a.j 2
7436.2.a.k 2
7436.2.a.l 3
7436.2.a.m 3
7436.2.a.n 3
7436.2.a.o 4
7436.2.a.p 4
7436.2.a.q 5
7436.2.a.r 5
7436.2.a.s 12
7436.2.a.t 12
7436.2.a.u 12
7436.2.a.v 12
7436.2.a.w 18
7436.2.a.x 18
7436.2.b \(\chi_{7436}(7435, \cdot)\) n/a 904 1
7436.2.e \(\chi_{7436}(6423, \cdot)\) n/a 908 1
7436.2.f \(\chi_{7436}(1013, \cdot)\) n/a 126 1
7436.2.i \(\chi_{7436}(529, \cdot)\) n/a 260 2
7436.2.j \(\chi_{7436}(2267, \cdot)\) n/a 1540 2
7436.2.m \(\chi_{7436}(1253, \cdot)\) n/a 308 2
7436.2.n \(\chi_{7436}(2029, \cdot)\) n/a 620 4
7436.2.p \(\chi_{7436}(485, \cdot)\) n/a 256 2
7436.2.s \(\chi_{7436}(2727, \cdot)\) n/a 1808 2
7436.2.t \(\chi_{7436}(3695, \cdot)\) n/a 1808 2
7436.2.x \(\chi_{7436}(3041, \cdot)\) n/a 616 4
7436.2.y \(\chi_{7436}(1691, \cdot)\) n/a 3632 4
7436.2.bb \(\chi_{7436}(2703, \cdot)\) n/a 3616 4
7436.2.bc \(\chi_{7436}(1033, \cdot)\) n/a 616 4
7436.2.bf \(\chi_{7436}(2047, \cdot)\) n/a 3080 4
7436.2.bg \(\chi_{7436}(573, \cdot)\) n/a 1824 12
7436.2.bh \(\chi_{7436}(653, \cdot)\) n/a 1232 8
7436.2.bi \(\chi_{7436}(437, \cdot)\) n/a 1232 8
7436.2.bl \(\chi_{7436}(775, \cdot)\) n/a 7232 8
7436.2.bo \(\chi_{7436}(441, \cdot)\) n/a 1848 12
7436.2.bp \(\chi_{7436}(131, \cdot)\) n/a 13056 12
7436.2.bs \(\chi_{7436}(571, \cdot)\) n/a 13056 12
7436.2.bu \(\chi_{7436}(315, \cdot)\) n/a 7232 8
7436.2.bv \(\chi_{7436}(699, \cdot)\) n/a 7232 8
7436.2.by \(\chi_{7436}(361, \cdot)\) n/a 1232 8
7436.2.ca \(\chi_{7436}(133, \cdot)\) n/a 3600 24
7436.2.cb \(\chi_{7436}(21, \cdot)\) n/a 4368 24
7436.2.ce \(\chi_{7436}(463, \cdot)\) n/a 21840 24
7436.2.cf \(\chi_{7436}(427, \cdot)\) n/a 14464 16
7436.2.ci \(\chi_{7436}(249, \cdot)\) n/a 2464 16
7436.2.cj \(\chi_{7436}(53, \cdot)\) n/a 8736 48
7436.2.cl \(\chi_{7436}(87, \cdot)\) n/a 26112 24
7436.2.cm \(\chi_{7436}(43, \cdot)\) n/a 26112 24
7436.2.cp \(\chi_{7436}(309, \cdot)\) n/a 3648 24
7436.2.cr \(\chi_{7436}(51, \cdot)\) n/a 52224 48
7436.2.cu \(\chi_{7436}(79, \cdot)\) n/a 52224 48
7436.2.cv \(\chi_{7436}(25, \cdot)\) n/a 8736 48
7436.2.cy \(\chi_{7436}(67, \cdot)\) n/a 43680 48
7436.2.db \(\chi_{7436}(197, \cdot)\) n/a 8736 48
7436.2.dc \(\chi_{7436}(9, \cdot)\) n/a 17472 96
7436.2.dd \(\chi_{7436}(31, \cdot)\) n/a 104448 96
7436.2.dg \(\chi_{7436}(57, \cdot)\) n/a 17472 96
7436.2.di \(\chi_{7436}(49, \cdot)\) n/a 17472 96
7436.2.dl \(\chi_{7436}(95, \cdot)\) n/a 104448 96
7436.2.dm \(\chi_{7436}(35, \cdot)\) n/a 104448 96
7436.2.do \(\chi_{7436}(41, \cdot)\) n/a 34944 192
7436.2.dr \(\chi_{7436}(15, \cdot)\) n/a 208896 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7436))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7436)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1859))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3718))\)\(^{\oplus 2}\)