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Properties

Label 675.4.u
Level $675$
Weight $4$
Character orbit 675.u
Rep. character $\chi_{675}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $960$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.u (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 1656 984 672
Cusp forms 1584 960 624
Eisenstein series 72 24 48

Trace form

\( 960 q + 12 q^{4} + 12 q^{6} - 84 q^{9} + O(q^{10}) \) \( 960 q + 12 q^{4} + 12 q^{6} - 84 q^{9} + 12 q^{11} + 276 q^{14} + 36 q^{16} + 6 q^{19} - 156 q^{21} - 150 q^{24} + 1848 q^{26} + 264 q^{29} - 120 q^{31} - 36 q^{34} - 4092 q^{36} - 672 q^{39} + 3228 q^{41} + 870 q^{44} - 6 q^{46} - 1176 q^{49} + 1890 q^{51} + 7260 q^{54} - 9114 q^{56} - 1812 q^{59} - 120 q^{61} + 28038 q^{64} + 6186 q^{66} - 6972 q^{69} - 5970 q^{71} - 2730 q^{74} + 372 q^{76} + 5628 q^{79} - 324 q^{81} + 23862 q^{84} + 17688 q^{86} + 6174 q^{89} - 6 q^{91} - 7332 q^{94} + 16968 q^{96} - 11040 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)