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Properties

Label 1025.2.x
Level $1025$
Weight $2$
Character orbit 1025.x
Rep. character $\chi_{1025}(646,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $408$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 1025 = 5^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1025.x (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1025 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(210\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1025, [\chi])\).

Total New Old
Modular forms 424 424 0
Cusp forms 408 408 0
Eisenstein series 16 16 0

Trace form

\( 408 q + q^{2} - 99 q^{4} + 3 q^{5} - 10 q^{7} + 6 q^{8} + 88 q^{9} + O(q^{10}) \) \( 408 q + q^{2} - 99 q^{4} + 3 q^{5} - 10 q^{7} + 6 q^{8} + 88 q^{9} - 33 q^{10} - 5 q^{11} - 5 q^{12} + 15 q^{13} - 15 q^{14} + 5 q^{15} - 89 q^{16} - 25 q^{17} - 5 q^{18} + 5 q^{19} + 15 q^{20} + 32 q^{21} + q^{23} + 20 q^{24} - 27 q^{25} - 25 q^{26} + 15 q^{28} - 15 q^{29} + 10 q^{30} + 11 q^{31} - 72 q^{32} - 16 q^{33} - 40 q^{34} - 5 q^{35} - 346 q^{36} - 12 q^{37} - 10 q^{38} - 24 q^{39} - 28 q^{40} + 15 q^{41} - 68 q^{42} - 2 q^{43} - 10 q^{44} + 28 q^{45} + 35 q^{46} + 30 q^{47} + 76 q^{49} + 30 q^{50} - 2 q^{51} + 110 q^{52} - 75 q^{53} + 40 q^{54} - 25 q^{55} - 25 q^{56} + 6 q^{57} + 5 q^{58} + 23 q^{59} + 70 q^{60} - 23 q^{61} - q^{62} - 10 q^{63} - 76 q^{64} - 45 q^{65} + 29 q^{66} - 85 q^{67} + 35 q^{70} - 40 q^{71} + 94 q^{72} + 8 q^{73} - 12 q^{74} + 55 q^{75} + 125 q^{76} - 74 q^{77} + 36 q^{78} + 10 q^{79} - 36 q^{80} - 88 q^{81} - 6 q^{82} - 9 q^{83} - 73 q^{84} - 142 q^{86} + 17 q^{87} - 20 q^{88} - 5 q^{89} + 20 q^{90} - 21 q^{91} + 105 q^{92} + 105 q^{93} - 5 q^{94} + 45 q^{95} - 105 q^{96} - 20 q^{97} + 65 q^{98} - 55 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1025, [\chi])\) into newform subspaces

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