Properties

Label 1425.2.bh
Level $1425$
Weight $2$
Character orbit 1425.bh
Rep. character $\chi_{1425}(106,\cdot)$
Character field $\Q(\zeta_{15})$
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.bh (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 800q + 100q^{4} + 2q^{5} - 8q^{7} - 36q^{8} + 100q^{9} + O(q^{10}) \) \( 800q + 100q^{4} + 2q^{5} - 8q^{7} - 36q^{8} + 100q^{9} - 6q^{10} + 12q^{11} + 8q^{13} - 12q^{14} - 2q^{15} + 100q^{16} - 6q^{17} - 6q^{19} - 44q^{20} + 8q^{21} - 48q^{22} - 12q^{23} + 2q^{25} + 40q^{26} + 4q^{28} + 12q^{29} - 32q^{30} - 48q^{31} - 44q^{32} + 6q^{33} + 16q^{34} + 12q^{35} + 100q^{36} + 16q^{37} - 4q^{38} + 14q^{40} + 80q^{43} - 68q^{44} - 4q^{45} + 16q^{46} + 4q^{47} + 792q^{49} - 84q^{50} - 64q^{51} + 32q^{52} - 36q^{53} - 38q^{55} - 72q^{56} - 8q^{57} + 60q^{58} + 48q^{59} + 16q^{60} + 16q^{61} + 14q^{62} - 6q^{63} - 188q^{64} + 36q^{65} - 128q^{67} + 24q^{68} - 24q^{69} - 20q^{70} + 8q^{71} + 18q^{72} - 56q^{73} + 8q^{75} + 48q^{76} - 136q^{77} - 40q^{78} + 32q^{79} + 26q^{80} + 100q^{81} - 68q^{82} + 76q^{83} - 48q^{84} + 18q^{85} + 60q^{86} + 96q^{87} - 184q^{88} - 12q^{89} + 24q^{90} + 32q^{91} + 48q^{92} - 192q^{93} - 124q^{94} + 82q^{95} + 20q^{96} + 10q^{97} + 104q^{98} + 4q^{99} + O(q^{100}) \)

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

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