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Properties

Label 1225.2.o
Level $1225$
Weight $2$
Character orbit 1225.o
Rep. character $\chi_{1225}(344,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $392$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.o (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1225, [\chi])\).

Total New Old
Modular forms 592 432 160
Cusp forms 528 392 136
Eisenstein series 64 40 24

Trace form

\( 392 q + 5 q^{2} + 5 q^{3} + 97 q^{4} + 6 q^{5} + 9 q^{6} - 40 q^{8} + 95 q^{9} + O(q^{10}) \) \( 392 q + 5 q^{2} + 5 q^{3} + 97 q^{4} + 6 q^{5} + 9 q^{6} - 40 q^{8} + 95 q^{9} + 9 q^{10} - 4 q^{11} + 25 q^{12} + 5 q^{13} - 37 q^{15} - 67 q^{16} + 10 q^{17} - 7 q^{19} + 3 q^{20} + 20 q^{22} - 5 q^{23} + 48 q^{24} + 4 q^{25} - 18 q^{26} - 25 q^{27} - 5 q^{29} - 51 q^{30} - 3 q^{31} - 30 q^{33} - 13 q^{34} - 141 q^{36} + 40 q^{37} + 55 q^{38} + 19 q^{39} + 20 q^{40} + 28 q^{44} + 67 q^{45} - 13 q^{46} + 10 q^{47} + 19 q^{50} + 12 q^{51} + 10 q^{52} - 80 q^{53} - 49 q^{54} + 12 q^{55} - 90 q^{58} + 6 q^{59} - 8 q^{60} + 13 q^{61} - 20 q^{62} + 2 q^{64} - 21 q^{65} + 62 q^{66} - 30 q^{67} + 61 q^{69} - 8 q^{71} - 115 q^{72} - 55 q^{73} - 32 q^{74} + 18 q^{75} - 32 q^{76} + 35 q^{78} - 19 q^{79} - 144 q^{80} - 58 q^{81} + 75 q^{83} - 21 q^{85} + 49 q^{86} - 10 q^{87} - 60 q^{88} - 13 q^{89} + 33 q^{90} - 200 q^{92} - 61 q^{94} + 117 q^{95} + 12 q^{96} + 90 q^{97} - 116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)