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Properties

Label 1425.2.bt
Level $1425$
Weight $2$
Character orbit 1425.bt
Rep. character $\chi_{1425}(64,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $800$
Sturm bound $400$

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Defining parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1425.bt (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1425, [\chi])\).

Total New Old
Modular forms 1632 800 832
Cusp forms 1568 800 768
Eisenstein series 64 0 64

Trace form

\( 800 q - 100 q^{4} + 2 q^{5} + 60 q^{8} - 100 q^{9} + O(q^{10}) \) \( 800 q - 100 q^{4} + 2 q^{5} + 60 q^{8} - 100 q^{9} + 6 q^{10} - 12 q^{11} - 12 q^{14} + 2 q^{15} + 100 q^{16} - 10 q^{17} - 6 q^{19} - 36 q^{20} - 8 q^{21} + 120 q^{22} + 60 q^{23} - 6 q^{25} - 40 q^{26} + 12 q^{29} - 32 q^{30} + 48 q^{31} + 10 q^{33} + 16 q^{34} + 20 q^{35} + 100 q^{36} + 60 q^{38} + 42 q^{40} - 68 q^{44} + 4 q^{45} - 16 q^{46} + 40 q^{47} - 808 q^{49} + 156 q^{50} + 64 q^{51} + 40 q^{53} - 114 q^{55} + 72 q^{56} - 380 q^{58} + 48 q^{59} - 32 q^{60} - 16 q^{61} + 50 q^{62} + 10 q^{63} + 212 q^{64} - 4 q^{65} + 80 q^{67} - 24 q^{69} + 36 q^{70} - 8 q^{71} - 30 q^{72} + 80 q^{73} + 8 q^{75} - 48 q^{76} + 80 q^{77} + 32 q^{79} - 50 q^{80} + 100 q^{81} + 140 q^{83} - 48 q^{84} + 54 q^{85} - 60 q^{86} + 160 q^{87} - 120 q^{88} - 12 q^{89} + 24 q^{90} - 32 q^{91} + 100 q^{92} - 164 q^{94} - 226 q^{95} + 20 q^{96} - 30 q^{97} - 80 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1425, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)