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Properties

Label 1350.4.u
Level $1350$
Weight $4$
Character orbit 1350.u
Rep. character $\chi_{1350}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $972$
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.u (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 4932 972 3960
Cusp forms 4788 972 3816
Eisenstein series 144 0 144

Trace form

\( 972 q - 24 q^{6} + 192 q^{9} + O(q^{10}) \) \( 972 q - 24 q^{6} + 192 q^{9} - 48 q^{11} - 264 q^{14} + 288 q^{21} - 1872 q^{26} - 84 q^{29} + 216 q^{31} + 1872 q^{36} - 288 q^{39} - 4008 q^{41} - 528 q^{44} + 1188 q^{49} - 1788 q^{51} + 1656 q^{54} + 1056 q^{56} + 2820 q^{59} + 108 q^{61} + 31104 q^{64} + 9480 q^{69} - 3648 q^{74} - 11232 q^{79} + 3720 q^{81} - 4320 q^{84} - 1044 q^{86} - 5928 q^{89} + 7344 q^{94} + 22044 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)