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Properties

Label 1343.2.f
Level $1343$
Weight $2$
Character orbit 1343.f
Rep. character $\chi_{1343}(633,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $236$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1343 = 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1343.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1343, [\chi])\).

Total New Old
Modular forms 244 236 8
Cusp forms 236 236 0
Eisenstein series 8 0 8

Trace form

\( 236 q - 4 q^{3} - 240 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} + O(q^{10}) \) \( 236 q - 4 q^{3} - 240 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} + 12 q^{10} + 8 q^{11} + 12 q^{12} - 16 q^{13} + 24 q^{14} + 248 q^{16} - 4 q^{17} - 8 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 8 q^{23} - 12 q^{24} + 20 q^{27} + 8 q^{28} + 4 q^{29} + 24 q^{30} - 40 q^{33} - 28 q^{34} - 56 q^{35} - 20 q^{37} - 16 q^{38} - 8 q^{39} + 24 q^{40} - 40 q^{44} + 16 q^{45} + 40 q^{47} - 92 q^{48} - 8 q^{50} - 20 q^{51} + 8 q^{52} + 40 q^{54} - 40 q^{55} - 44 q^{56} + 28 q^{57} - 12 q^{58} - 4 q^{61} - 40 q^{62} + 32 q^{63} - 264 q^{64} - 4 q^{65} + 16 q^{67} - 4 q^{68} - 24 q^{69} + 56 q^{71} + 88 q^{72} + 12 q^{73} + 84 q^{74} - 16 q^{75} - 100 q^{78} - 4 q^{80} - 212 q^{81} + 72 q^{82} - 16 q^{84} + 28 q^{85} + 16 q^{86} - 4 q^{88} - 56 q^{89} + 80 q^{90} - 88 q^{91} + 40 q^{92} + 36 q^{95} + 4 q^{96} + 12 q^{97} + 136 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1343, [\chi])\) into newform subspaces

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