Properties

Label 4332.2
Level 4332
Weight 2
Dimension 225234
Nonzero newspaces 24
Sturm bound 2079360

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Defining parameters

Level: \( N \) = \( 4332 = 2^{2} \cdot 3 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(2079360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4332))\).

Total New Old
Modular forms 524880 227110 297770
Cusp forms 514801 225234 289567
Eisenstein series 10079 1876 8203

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4332))\)

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
4332.2.a \(\chi_{4332}(1, \cdot)\) 4332.2.a.a 1 1
4332.2.a.b 1
4332.2.a.c 1
4332.2.a.d 1
4332.2.a.e 2
4332.2.a.f 2
4332.2.a.g 2
4332.2.a.h 2
4332.2.a.i 2
4332.2.a.j 2
4332.2.a.k 2
4332.2.a.l 2
4332.2.a.m 2
4332.2.a.n 3
4332.2.a.o 3
4332.2.a.p 4
4332.2.a.q 4
4332.2.a.r 4
4332.2.a.s 4
4332.2.a.t 6
4332.2.a.u 6
4332.2.c \(\chi_{4332}(3611, \cdot)\) n/a 648 1
4332.2.d \(\chi_{4332}(2165, \cdot)\) n/a 114 1
4332.2.f \(\chi_{4332}(2887, \cdot)\) n/a 340 1
4332.2.i \(\chi_{4332}(1873, \cdot)\) n/a 112 2
4332.2.k \(\chi_{4332}(1015, \cdot)\) n/a 680 2
4332.2.m \(\chi_{4332}(1151, \cdot)\) n/a 1296 2
4332.2.p \(\chi_{4332}(293, \cdot)\) n/a 228 2
4332.2.q \(\chi_{4332}(2581, \cdot)\) n/a 342 6
4332.2.t \(\chi_{4332}(2465, \cdot)\) n/a 678 6
4332.2.v \(\chi_{4332}(1859, \cdot)\) n/a 3888 6
4332.2.w \(\chi_{4332}(127, \cdot)\) n/a 2040 6
4332.2.y \(\chi_{4332}(229, \cdot)\) n/a 1152 18
4332.2.bb \(\chi_{4332}(151, \cdot)\) n/a 6840 18
4332.2.bd \(\chi_{4332}(113, \cdot)\) n/a 2268 18
4332.2.be \(\chi_{4332}(191, \cdot)\) n/a 13608 18
4332.2.bg \(\chi_{4332}(49, \cdot)\) n/a 2304 36
4332.2.bh \(\chi_{4332}(65, \cdot)\) n/a 4536 36
4332.2.bk \(\chi_{4332}(11, \cdot)\) n/a 27216 36
4332.2.bm \(\chi_{4332}(31, \cdot)\) n/a 13680 36
4332.2.bo \(\chi_{4332}(25, \cdot)\) n/a 6804 108
4332.2.bq \(\chi_{4332}(67, \cdot)\) n/a 41040 108
4332.2.br \(\chi_{4332}(23, \cdot)\) n/a 81648 108
4332.2.bt \(\chi_{4332}(29, \cdot)\) n/a 13716 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)\(^{\oplus 2}\)