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Properties

Label 1575.2.co
Level $1575$
Weight $2$
Character orbit 1575.co
Rep. character $\chi_{1575}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
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.co (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560 q - 2 q^{2} + 6 q^{3} + 2 q^{7} + 8 q^{8} + O(q^{10}) \) \( 560 q - 2 q^{2} + 6 q^{3} + 2 q^{7} + 8 q^{8} - 24 q^{11} + 6 q^{12} + 260 q^{16} + 30 q^{17} + 26 q^{18} + 48 q^{21} + 12 q^{22} - 12 q^{23} - 24 q^{26} - 36 q^{27} - 4 q^{28} - 12 q^{31} - 30 q^{32} - 24 q^{33} - 80 q^{36} + 4 q^{37} + 24 q^{41} + 10 q^{42} + 4 q^{43} + 16 q^{46} + 6 q^{47} + 18 q^{48} + 44 q^{51} - 16 q^{53} + 68 q^{56} - 8 q^{57} + 44 q^{58} + 60 q^{61} - 54 q^{63} - 84 q^{66} - 2 q^{67} + 32 q^{71} - 10 q^{72} + 12 q^{73} - 48 q^{76} + 106 q^{77} + 62 q^{78} - 52 q^{81} + 24 q^{82} - 84 q^{83} - 184 q^{86} + 24 q^{87} + 84 q^{88} - 16 q^{91} + 8 q^{92} - 28 q^{93} - 180 q^{96} - 120 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)