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Properties

Label 4356.2
Level 4356
Weight 2
Dimension 236158
Nonzero newspaces 32
Sturm bound 2090880

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Defining parameters

Level: \( N \) = \( 4356 = 2^{2} \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2090880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4356))\).

Total New Old
Modular forms 529120 238686 290434
Cusp forms 516321 236158 280163
Eisenstein series 12799 2528 10271

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4356))\)

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
4356.2.a \(\chi_{4356}(1, \cdot)\) 4356.2.a.a 1 1
4356.2.a.b 1
4356.2.a.c 1
4356.2.a.d 1
4356.2.a.e 1
4356.2.a.f 1
4356.2.a.g 1
4356.2.a.h 1
4356.2.a.i 1
4356.2.a.j 1
4356.2.a.k 1
4356.2.a.l 1
4356.2.a.m 2
4356.2.a.n 2
4356.2.a.o 2
4356.2.a.p 2
4356.2.a.q 2
4356.2.a.r 2
4356.2.a.s 2
4356.2.a.t 2
4356.2.a.u 2
4356.2.a.v 2
4356.2.a.w 2
4356.2.a.x 4
4356.2.a.y 4
4356.2.a.z 4
4356.2.b \(\chi_{4356}(2177, \cdot)\) 4356.2.b.a 2 1
4356.2.b.b 2
4356.2.b.c 8
4356.2.b.d 8
4356.2.b.e 16
4356.2.c \(\chi_{4356}(2663, \cdot)\) n/a 218 1
4356.2.h \(\chi_{4356}(3871, \cdot)\) n/a 262 1
4356.2.i \(\chi_{4356}(1453, \cdot)\) n/a 218 2
4356.2.j \(\chi_{4356}(1945, \cdot)\) n/a 180 4
4356.2.k \(\chi_{4356}(967, \cdot)\) n/a 1264 2
4356.2.p \(\chi_{4356}(1211, \cdot)\) n/a 1272 2
4356.2.q \(\chi_{4356}(725, \cdot)\) n/a 216 2
4356.2.r \(\chi_{4356}(1207, \cdot)\) n/a 1048 4
4356.2.w \(\chi_{4356}(251, \cdot)\) n/a 864 4
4356.2.x \(\chi_{4356}(161, \cdot)\) n/a 144 4
4356.2.y \(\chi_{4356}(397, \cdot)\) n/a 550 10
4356.2.z \(\chi_{4356}(493, \cdot)\) n/a 864 8
4356.2.ba \(\chi_{4356}(307, \cdot)\) n/a 3280 10
4356.2.bf \(\chi_{4356}(287, \cdot)\) n/a 2640 10
4356.2.bg \(\chi_{4356}(197, \cdot)\) n/a 440 10
4356.2.bh \(\chi_{4356}(941, \cdot)\) n/a 864 8
4356.2.bi \(\chi_{4356}(995, \cdot)\) n/a 5056 8
4356.2.bn \(\chi_{4356}(403, \cdot)\) n/a 5056 8
4356.2.bo \(\chi_{4356}(133, \cdot)\) n/a 2640 20
4356.2.bp \(\chi_{4356}(37, \cdot)\) n/a 2200 40
4356.2.bq \(\chi_{4356}(65, \cdot)\) n/a 2640 20
4356.2.br \(\chi_{4356}(23, \cdot)\) n/a 15760 20
4356.2.bw \(\chi_{4356}(43, \cdot)\) n/a 15760 20
4356.2.bx \(\chi_{4356}(17, \cdot)\) n/a 1760 40
4356.2.by \(\chi_{4356}(71, \cdot)\) n/a 10560 40
4356.2.cd \(\chi_{4356}(19, \cdot)\) n/a 13120 40
4356.2.ce \(\chi_{4356}(25, \cdot)\) n/a 10560 80
4356.2.cf \(\chi_{4356}(7, \cdot)\) n/a 63040 80
4356.2.ck \(\chi_{4356}(47, \cdot)\) n/a 63040 80
4356.2.cl \(\chi_{4356}(29, \cdot)\) n/a 10560 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4356))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4356)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1452))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2178))\)\(^{\oplus 2}\)