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Properties

Label 675.4.h
Level $675$
Weight $4$
Character orbit 675.h
Rep. character $\chi_{675}(136,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $480$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(675, [\chi])\).

Total New Old
Modular forms 1104 480 624
Cusp forms 1056 480 576
Eisenstein series 48 0 48

Trace form

\( 480 q - 480 q^{4} - 12 q^{7} + O(q^{10}) \) \( 480 q - 480 q^{4} - 12 q^{7} + 24 q^{10} - 96 q^{13} - 2028 q^{16} - 36 q^{19} + 600 q^{22} - 666 q^{25} - 216 q^{28} - 414 q^{31} + 1440 q^{34} - 2160 q^{37} + 1878 q^{40} + 1224 q^{43} - 1068 q^{46} + 24900 q^{49} - 318 q^{52} + 966 q^{55} + 2196 q^{58} - 1440 q^{61} - 9480 q^{64} - 840 q^{67} + 6054 q^{70} - 756 q^{73} + 5280 q^{76} - 24 q^{79} + 684 q^{82} + 15312 q^{85} - 2964 q^{88} + 1332 q^{91} - 7458 q^{94} + 4434 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)