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Properties

Label 405.4.f
Level $405$
Weight $4$
Character orbit 405.f
Rep. character $\chi_{405}(242,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $136$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(405, [\chi])\).

Total New Old
Modular forms 348 152 196
Cusp forms 300 136 164
Eisenstein series 48 16 32

Trace form

\( 136 q + 4 q^{7} + O(q^{10}) \) \( 136 q + 4 q^{7} - 8 q^{10} + 40 q^{13} - 1784 q^{16} + 68 q^{22} + 292 q^{25} - 232 q^{28} + 8 q^{31} - 1052 q^{37} + 612 q^{40} + 1012 q^{43} - 1096 q^{46} + 52 q^{52} + 284 q^{55} - 708 q^{58} - 64 q^{61} - 1220 q^{67} - 5964 q^{70} - 1052 q^{73} + 1728 q^{76} + 464 q^{82} + 5656 q^{85} - 5676 q^{88} + 5168 q^{91} - 1508 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(405, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)