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Properties

Label 1350.4.m
Level $1350$
Weight $4$
Character orbit 1350.m
Rep. character $\chi_{1350}(109,\cdot)$
Character field $\Q(\zeta_{10})$
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.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 480 q + 480 q^{4} + O(q^{10}) \) \( 480 q + 480 q^{4} + 36 q^{10} - 1920 q^{16} + 72 q^{19} - 360 q^{22} - 702 q^{25} - 120 q^{28} - 414 q^{31} - 1584 q^{34} - 1320 q^{37} - 144 q^{40} - 648 q^{46} - 25260 q^{49} + 1770 q^{55} + 240 q^{61} + 7680 q^{64} - 720 q^{67} - 3516 q^{70} - 600 q^{73} + 192 q^{76} - 624 q^{79} + 8160 q^{85} - 1680 q^{88} + 2520 q^{91} - 96 q^{94} - 930 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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