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Properties

Label 1343.2.m
Level $1343$
Weight $2$
Character orbit 1343.m
Rep. character $\chi_{1343}(55,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $472$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1343 = 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1343.m (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1343 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 2 q^{3} + 228 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + O(q^{10}) \) \( 472 q - 2 q^{3} + 228 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 14 q^{11} + 36 q^{12} - 8 q^{13} - 36 q^{14} - 236 q^{16} - 8 q^{17} - 16 q^{18} + 18 q^{20} - 80 q^{21} - 16 q^{22} - 4 q^{23} + 6 q^{24} - 32 q^{27} + 28 q^{28} + 2 q^{29} - 12 q^{30} - 32 q^{33} + 10 q^{34} + 20 q^{35} + 14 q^{37} - 80 q^{38} - 34 q^{39} - 24 q^{40} - 12 q^{41} + 76 q^{44} - 22 q^{45} - 12 q^{46} - 40 q^{47} + 20 q^{48} - 28 q^{50} - 10 q^{51} - 32 q^{52} + 32 q^{54} - 20 q^{55} - 34 q^{56} - 88 q^{57} - 104 q^{61} + 28 q^{62} - 86 q^{63} - 480 q^{64} - 8 q^{65} + 32 q^{67} - 14 q^{68} - 240 q^{69} - 32 q^{71} + 20 q^{72} - 18 q^{73} + 30 q^{74} + 40 q^{75} - 8 q^{78} + 30 q^{79} + 88 q^{80} + 200 q^{81} + 66 q^{82} - 116 q^{84} + 14 q^{85} + 44 q^{86} - 14 q^{88} - 40 q^{89} + 112 q^{90} + 124 q^{91} + 44 q^{92} + 18 q^{95} + 176 q^{96} - 72 q^{97} - 40 q^{98} - 92 q^{99} + O(q^{100}) \)

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.