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Properties

Label 1225.2.x
Level $1225$
Weight $2$
Character orbit 1225.x
Rep. character $\chi_{1225}(51,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1032$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1225.x (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(280\)

Dimensions

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

Total New Old
Modular forms 1752 1104 648
Cusp forms 1608 1032 576
Eisenstein series 144 72 72

Trace form

\( 1032 q + 13 q^{2} + 12 q^{3} + 97 q^{4} - 40 q^{6} + 16 q^{7} + 20 q^{8} + 78 q^{9} + O(q^{10}) \) \( 1032 q + 13 q^{2} + 12 q^{3} + 97 q^{4} - 40 q^{6} + 16 q^{7} + 20 q^{8} + 78 q^{9} - 49 q^{11} + 55 q^{12} + 6 q^{13} + 27 q^{14} + 35 q^{16} + 3 q^{17} + 16 q^{18} - 17 q^{19} - 24 q^{21} - 12 q^{22} + 33 q^{23} + 44 q^{24} - 34 q^{26} + 39 q^{27} + 34 q^{28} - 20 q^{29} - 61 q^{31} - 25 q^{32} + 2 q^{33} - 54 q^{34} - 260 q^{36} + 35 q^{37} - 36 q^{38} - 11 q^{39} - 10 q^{41} - 58 q^{42} + 26 q^{43} + 80 q^{44} + 36 q^{46} + 3 q^{47} - 16 q^{48} + 62 q^{49} + 26 q^{51} - 22 q^{52} - 43 q^{53} + 123 q^{54} + 130 q^{56} - 20 q^{57} - 106 q^{58} + 30 q^{59} - 31 q^{61} - 52 q^{62} + 63 q^{63} - 160 q^{64} - 22 q^{66} - 5 q^{67} + 71 q^{68} + 50 q^{69} - 103 q^{71} - 104 q^{72} + 31 q^{73} - 30 q^{74} - 131 q^{76} + 63 q^{77} + 16 q^{78} + 11 q^{79} - 154 q^{81} - 108 q^{82} + 46 q^{83} - 202 q^{84} - 207 q^{86} - 110 q^{87} + 207 q^{88} - 56 q^{89} - 46 q^{91} + 82 q^{92} + 116 q^{93} - 128 q^{94} - 280 q^{96} - 88 q^{97} + 203 q^{98} - 76 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)