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Properties

Label 1343.2.w
Level $1343$
Weight $2$
Character orbit 1343.w
Rep. character $\chi_{1343}(171,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $2544$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1343 = 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1343.w (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 79 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 2928 2544 384
Cusp forms 2832 2544 288
Eisenstein series 96 0 96

Trace form

\( 2544 q - 2 q^{2} + 2 q^{3} + 102 q^{4} + 4 q^{6} + 2 q^{7} - 52 q^{8} + 104 q^{9} + O(q^{10}) \) \( 2544 q - 2 q^{2} + 2 q^{3} + 102 q^{4} + 4 q^{6} + 2 q^{7} - 52 q^{8} + 104 q^{9} - 24 q^{10} - 56 q^{11} + 8 q^{12} - 2 q^{13} - 12 q^{14} + 24 q^{15} + 78 q^{16} - 8 q^{17} + 24 q^{18} - 2 q^{19} + 38 q^{20} - 8 q^{21} - 84 q^{22} - 16 q^{23} - 158 q^{24} - 58 q^{25} + 18 q^{26} - 40 q^{27} - 14 q^{28} + 36 q^{29} - 42 q^{30} - 58 q^{31} + 8 q^{32} + 32 q^{33} + 4 q^{34} + 16 q^{35} + 86 q^{36} + 14 q^{37} + 20 q^{38} + 4 q^{39} - 82 q^{40} - 12 q^{41} - 24 q^{42} - 18 q^{43} - 18 q^{44} - 28 q^{45} - 52 q^{46} - 22 q^{47} + 20 q^{48} + 84 q^{49} - 102 q^{50} - 60 q^{52} - 90 q^{53} + 12 q^{54} + 48 q^{55} - 256 q^{56} - 360 q^{57} + 64 q^{58} - 52 q^{59} - 582 q^{60} + 32 q^{62} - 132 q^{63} - 256 q^{64} + 36 q^{65} - 368 q^{66} + 26 q^{67} + 12 q^{68} - 44 q^{69} + 320 q^{70} + 16 q^{71} + 528 q^{72} + 72 q^{73} - 108 q^{74} + 34 q^{75} + 218 q^{76} - 316 q^{77} + 76 q^{78} - 46 q^{79} + 404 q^{80} + 138 q^{81} + 196 q^{82} - 352 q^{83} + 190 q^{84} + 4 q^{85} - 232 q^{86} - 126 q^{87} + 470 q^{88} + 100 q^{89} + 176 q^{90} - 34 q^{91} + 28 q^{92} - 66 q^{93} - 288 q^{94} + 84 q^{95} - 436 q^{96} - 170 q^{97} + 14 q^{98} - 116 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1343, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1343, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)