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Properties

Label 1421.2.ci
Level $1421$
Weight $2$
Character orbit 1421.ci
Rep. character $\chi_{1421}(55,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1656$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 1421 = 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1421.ci (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1421, [\chi])\).

Total New Old
Modular forms 1704 1704 0
Cusp forms 1656 1656 0
Eisenstein series 48 48 0

Trace form

\( 1656 q - 10 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} - 18 q^{8} - 14 q^{9} + O(q^{10}) \) \( 1656 q - 10 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} - 18 q^{8} - 14 q^{9} - 14 q^{10} - 10 q^{11} - 56 q^{12} - 14 q^{13} - 16 q^{14} - 20 q^{15} + 258 q^{16} + 8 q^{18} - 70 q^{20} - 54 q^{21} - 14 q^{22} - 20 q^{23} + 42 q^{24} - 266 q^{25} - 14 q^{26} - 14 q^{27} + 112 q^{28} - 42 q^{29} + 56 q^{30} + 88 q^{32} - 14 q^{33} - 14 q^{34} - 14 q^{35} - 258 q^{36} + 28 q^{38} - 22 q^{39} - 42 q^{40} + 14 q^{41} + 70 q^{42} + 6 q^{43} + 76 q^{44} - 14 q^{45} - 74 q^{46} - 14 q^{47} - 58 q^{49} - 48 q^{50} - 14 q^{51} + 70 q^{52} - 126 q^{53} + 126 q^{55} - 78 q^{56} + 22 q^{58} + 14 q^{59} - 180 q^{60} - 14 q^{61} - 14 q^{62} - 238 q^{63} - 14 q^{64} + 80 q^{65} + 154 q^{66} - 28 q^{67} + 14 q^{68} - 210 q^{69} - 60 q^{70} - 56 q^{71} - 82 q^{72} - 56 q^{73} - 68 q^{74} - 84 q^{75} - 14 q^{76} + 48 q^{77} + 18 q^{78} + 8 q^{79} + 222 q^{81} - 14 q^{82} - 14 q^{83} + 18 q^{84} - 44 q^{85} + 84 q^{86} - 14 q^{87} - 128 q^{88} - 14 q^{89} - 56 q^{90} - 70 q^{91} - 126 q^{92} - 98 q^{93} + 182 q^{94} + 10 q^{95} - 28 q^{96} + 84 q^{97} + 44 q^{98} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1421, [\chi])\) into newform subspaces

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