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Properties

Label 1350.4.e
Level $1350$
Weight $4$
Character orbit 1350.e
Rep. character $\chi_{1350}(451,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $114$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 1692 114 1578
Cusp forms 1548 114 1434
Eisenstein series 144 0 144

Trace form

\( 114 q - 2 q^{2} - 228 q^{4} + 12 q^{7} + 16 q^{8} + O(q^{10}) \) \( 114 q - 2 q^{2} - 228 q^{4} + 12 q^{7} + 16 q^{8} - 11 q^{11} - 24 q^{13} + 100 q^{14} - 912 q^{16} + 270 q^{17} + 210 q^{19} - 18 q^{22} - 96 q^{23} - 232 q^{26} - 96 q^{28} - 108 q^{29} + 66 q^{31} - 32 q^{32} + 90 q^{34} + 480 q^{37} - 346 q^{38} + 763 q^{41} + 129 q^{43} + 88 q^{44} - 504 q^{46} + 288 q^{47} - 2835 q^{49} - 96 q^{52} + 1848 q^{53} + 400 q^{56} - 252 q^{58} + 1133 q^{59} + 822 q^{61} - 304 q^{62} + 7296 q^{64} + 363 q^{67} - 540 q^{68} - 7032 q^{71} - 258 q^{73} + 16 q^{74} - 420 q^{76} - 1812 q^{77} + 642 q^{79} + 828 q^{82} - 690 q^{83} - 446 q^{86} - 72 q^{88} - 5564 q^{89} + 492 q^{91} - 384 q^{92} - 612 q^{94} - 2067 q^{97} + 372 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)