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Properties

Label 1425.2.n
Level $1425$
Weight $2$
Character orbit 1425.n
Rep. character $\chi_{1425}(286,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $352$
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.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(400\)

Dimensions

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

Total New Old
Modular forms 816 352 464
Cusp forms 784 352 432
Eisenstein series 32 0 32

Trace form

\( 352 q + 4 q^{2} - 84 q^{4} + 10 q^{5} + 4 q^{6} + 12 q^{7} + 12 q^{8} - 88 q^{9} + O(q^{10}) \) \( 352 q + 4 q^{2} - 84 q^{4} + 10 q^{5} + 4 q^{6} + 12 q^{7} + 12 q^{8} - 88 q^{9} + 16 q^{10} - 6 q^{11} + 16 q^{12} + 16 q^{13} + 4 q^{15} - 100 q^{16} + 26 q^{17} - 16 q^{18} + 8 q^{19} - 72 q^{20} + 24 q^{22} - 24 q^{23} - 48 q^{24} + 30 q^{25} + 24 q^{26} + 12 q^{28} + 32 q^{29} - 56 q^{30} - 12 q^{31} - 112 q^{32} + 24 q^{33} - 4 q^{34} + 12 q^{35} - 84 q^{36} + 16 q^{39} + 4 q^{40} + 12 q^{41} + 28 q^{42} + 36 q^{43} + 16 q^{44} + 10 q^{45} + 40 q^{46} + 28 q^{47} + 64 q^{48} + 316 q^{49} - 124 q^{50} - 112 q^{52} - 72 q^{53} + 4 q^{54} + 46 q^{55} + 72 q^{56} + 80 q^{58} - 28 q^{60} + 60 q^{61} + 2 q^{63} - 108 q^{64} - 60 q^{65} + 32 q^{66} + 32 q^{67} + 176 q^{68} + 64 q^{70} + 12 q^{72} + 68 q^{73} + 144 q^{74} + 40 q^{75} - 80 q^{76} + 116 q^{77} - 16 q^{79} + 144 q^{80} - 88 q^{81} - 144 q^{82} - 24 q^{83} - 48 q^{84} - 56 q^{85} + 48 q^{86} + 32 q^{87} - 200 q^{88} - 120 q^{89} + 16 q^{90} + 20 q^{91} - 68 q^{92} + 16 q^{93} - 24 q^{94} + 2 q^{95} - 32 q^{96} + 20 q^{97} - 44 q^{98} + 4 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)