Properties

Label 405.4
Level 405
Weight 4
Dimension 12504
Nonzero newspaces 12
Sturm bound 46656
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(46656\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(405))\).

Total New Old
Modular forms 17928 12840 5088
Cusp forms 17064 12504 4560
Eisenstein series 864 336 528

Trace form

\( 12504 q - 24 q^{2} - 36 q^{3} - 24 q^{4} - 24 q^{5} - 108 q^{6} - 76 q^{7} - 162 q^{8} - 36 q^{9} - 107 q^{10} + 54 q^{11} - 36 q^{12} + 68 q^{13} + 90 q^{14} - 54 q^{15} - 464 q^{16} - 426 q^{17} - 864 q^{18}+ \cdots + 26388 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(405))\)

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
405.4.a \(\chi_{405}(1, \cdot)\) 405.4.a.a 1 1
405.4.a.b 1
405.4.a.c 2
405.4.a.d 2
405.4.a.e 2
405.4.a.f 2
405.4.a.g 3
405.4.a.h 3
405.4.a.i 3
405.4.a.j 3
405.4.a.k 6
405.4.a.l 6
405.4.a.m 7
405.4.a.n 7
405.4.b \(\chi_{405}(244, \cdot)\) 405.4.b.a 4 1
405.4.b.b 8
405.4.b.c 8
405.4.b.d 16
405.4.b.e 16
405.4.b.f 16
405.4.e \(\chi_{405}(136, \cdot)\) 405.4.e.a 2 2
405.4.e.b 2
405.4.e.c 2
405.4.e.d 2
405.4.e.e 2
405.4.e.f 2
405.4.e.g 2
405.4.e.h 2
405.4.e.i 2
405.4.e.j 2
405.4.e.k 2
405.4.e.l 2
405.4.e.m 2
405.4.e.n 2
405.4.e.o 4
405.4.e.p 4
405.4.e.q 6
405.4.e.r 6
405.4.e.s 6
405.4.e.t 6
405.4.e.u 6
405.4.e.v 6
405.4.e.w 12
405.4.e.x 12
405.4.f \(\chi_{405}(242, \cdot)\) n/a 136 2
405.4.j \(\chi_{405}(109, \cdot)\) n/a 140 2
405.4.k \(\chi_{405}(46, \cdot)\) n/a 216 6
405.4.m \(\chi_{405}(53, \cdot)\) n/a 280 4
405.4.p \(\chi_{405}(19, \cdot)\) n/a 312 6
405.4.q \(\chi_{405}(16, \cdot)\) n/a 1944 18
405.4.r \(\chi_{405}(8, \cdot)\) n/a 624 12
405.4.t \(\chi_{405}(4, \cdot)\) n/a 2880 18
405.4.x \(\chi_{405}(2, \cdot)\) n/a 5760 36

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(405))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(405)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)