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Properties

Label 675.4.ba
Level $675$
Weight $4$
Character orbit 675.ba
Rep. character $\chi_{675}(32,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1920$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.ba (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 3312 1968 1344
Cusp forms 3168 1920 1248
Eisenstein series 144 48 96

Trace form

\( 1920 q + 12 q^{2} + 12 q^{3} - 72 q^{6} + 12 q^{7} + 18 q^{8} + O(q^{10}) \) \( 1920 q + 12 q^{2} + 12 q^{3} - 72 q^{6} + 12 q^{7} + 18 q^{8} - 72 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} - 702 q^{18} - 24 q^{21} + 12 q^{22} + 324 q^{23} + 900 q^{27} + 24 q^{28} - 24 q^{31} - 1752 q^{32} - 516 q^{33} - 2040 q^{36} + 6 q^{37} + 132 q^{38} - 3432 q^{41} + 2256 q^{42} + 12 q^{43} - 12 q^{46} + 3480 q^{47} + 3228 q^{48} - 3312 q^{51} - 84 q^{52} + 9432 q^{56} - 1842 q^{57} + 12 q^{58} + 192 q^{61} + 18 q^{62} - 2592 q^{63} - 19800 q^{66} - 3660 q^{67} - 2676 q^{68} - 36 q^{71} - 1908 q^{72} + 6 q^{73} - 792 q^{76} + 3324 q^{77} + 606 q^{78} + 6600 q^{81} + 24 q^{82} + 2832 q^{83} + 14520 q^{86} + 8640 q^{87} + 3036 q^{88} - 12 q^{91} + 1938 q^{92} - 6804 q^{93} - 7536 q^{96} - 6900 q^{97} + 5832 q^{98} + O(q^{100}) \)

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

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