Properties

Label 1350.4.h
Level $1350$
Weight $4$
Character orbit 1350.h
Rep. character $\chi_{1350}(271,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $480$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1350.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1350, [\chi])\).

Total New Old
Modular forms 3288 480 2808
Cusp forms 3192 480 2712
Eisenstein series 96 0 96

Trace form

\( 480 q - 480 q^{4} + 12 q^{7} + O(q^{10}) \) \( 480 q - 480 q^{4} + 12 q^{7} - 60 q^{10} + 144 q^{13} - 1920 q^{16} + 72 q^{19} - 384 q^{22} + 774 q^{25} - 72 q^{28} + 414 q^{31} - 1584 q^{34} + 576 q^{37} - 240 q^{40} - 3312 q^{43} + 648 q^{46} + 21780 q^{49} + 576 q^{52} - 1158 q^{55} + 864 q^{58} - 240 q^{61} - 7680 q^{64} + 600 q^{67} - 1692 q^{70} + 2412 q^{73} - 192 q^{76} - 624 q^{79} - 2400 q^{82} - 13416 q^{85} + 1584 q^{88} - 2520 q^{91} - 96 q^{94} - 1086 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)