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Properties

Label 1575.2.j
Level $1575$
Weight $2$
Character orbit 1575.j
Rep. character $\chi_{1575}(226,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $120$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 528 132 396
Cusp forms 432 120 312
Eisenstein series 96 12 84

Trace form

\( 120 q - 54 q^{4} - 12 q^{8} + O(q^{10}) \) \( 120 q - 54 q^{4} - 12 q^{8} + 10 q^{11} - 4 q^{13} - 12 q^{14} - 42 q^{16} - 12 q^{17} + 6 q^{19} - 16 q^{22} + 10 q^{23} - 2 q^{28} - 20 q^{31} + 22 q^{32} + 48 q^{34} + 14 q^{37} + 22 q^{38} - 16 q^{41} + 16 q^{43} + 64 q^{44} - 6 q^{47} + 2 q^{49} + 44 q^{52} - 20 q^{53} + 6 q^{56} - 2 q^{58} + 30 q^{59} - 6 q^{61} + 36 q^{62} - 16 q^{67} - 8 q^{68} - 8 q^{71} + 22 q^{73} - 24 q^{74} - 76 q^{76} + 64 q^{77} - 22 q^{82} + 24 q^{83} + 6 q^{86} + 76 q^{88} - 16 q^{89} + 32 q^{91} - 76 q^{92} - 54 q^{94} + 8 q^{97} - 10 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)