Properties

Label 414.4
Level 414
Weight 4
Dimension 3748
Nonzero newspaces 8
Sturm bound 38016
Trace bound 3

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Defining parameters

Level: \( N \) = \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(38016\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(414))\).

Total New Old
Modular forms 14608 3748 10860
Cusp forms 13904 3748 10156
Eisenstein series 704 0 704

Trace form

\( 3748 q - 8 q^{2} - 6 q^{3} + 16 q^{4} - 24 q^{5} + 36 q^{6} + 8 q^{7} + 16 q^{8} + 210 q^{9} + 24 q^{10} - 54 q^{11} - 48 q^{12} - 28 q^{13} - 136 q^{14} - 180 q^{15} + 64 q^{16} + 80 q^{17} - 312 q^{18}+ \cdots - 2304 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(414))\)

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
414.4.a \(\chi_{414}(1, \cdot)\) 414.4.a.a 1 1
414.4.a.b 1
414.4.a.c 1
414.4.a.d 1
414.4.a.e 1
414.4.a.f 2
414.4.a.g 2
414.4.a.h 2
414.4.a.i 2
414.4.a.j 2
414.4.a.k 2
414.4.a.l 3
414.4.a.m 4
414.4.a.n 4
414.4.d \(\chi_{414}(413, \cdot)\) 414.4.d.a 24 1
414.4.e \(\chi_{414}(139, \cdot)\) n/a 132 2
414.4.f \(\chi_{414}(137, \cdot)\) n/a 144 2
414.4.i \(\chi_{414}(55, \cdot)\) n/a 300 10
414.4.j \(\chi_{414}(17, \cdot)\) n/a 240 10
414.4.m \(\chi_{414}(13, \cdot)\) n/a 1440 20
414.4.p \(\chi_{414}(5, \cdot)\) n/a 1440 20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(414))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(414)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)