Properties

Label 1343.2.bk
Level $1343$
Weight $2$
Character orbit 1343.bk
Rep. character $\chi_{1343}(2,\cdot)$
Character field $\Q(\zeta_{312})$
Dimension $11328$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1343 = 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1343.bk (of order \(312\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1343 \)
Character field: \(\Q(\zeta_{312})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 11712 11712 0
Cusp forms 11328 11328 0
Eisenstein series 384 384 0

Trace form

\( 11328 q - 100 q^{2} - 100 q^{3} - 100 q^{5} - 84 q^{6} - 100 q^{7} - 72 q^{8} - 100 q^{9} + O(q^{10}) \) \( 11328 q - 100 q^{2} - 100 q^{3} - 100 q^{5} - 84 q^{6} - 100 q^{7} - 72 q^{8} - 100 q^{9} - 88 q^{10} - 100 q^{11} - 64 q^{12} - 88 q^{14} - 200 q^{15} - 648 q^{16} - 88 q^{17} - 208 q^{18} - 116 q^{19} - 68 q^{20} - 88 q^{22} - 44 q^{23} - 52 q^{24} - 100 q^{25} - 84 q^{26} - 88 q^{27} - 68 q^{28} - 100 q^{29} - 84 q^{31} + 68 q^{32} - 80 q^{33} - 36 q^{34} - 120 q^{35} - 124 q^{36} + 76 q^{37} - 52 q^{39} - 148 q^{40} - 88 q^{41} - 352 q^{42} - 100 q^{43} + 316 q^{44} - 112 q^{45} - 456 q^{46} - 272 q^{48} - 132 q^{49} - 424 q^{50} - 148 q^{51} - 112 q^{52} - 92 q^{53} - 420 q^{54} - 4 q^{56} - 152 q^{57} - 56 q^{58} - 84 q^{59} - 48 q^{60} - 216 q^{61} - 64 q^{63} - 64 q^{65} + 308 q^{66} - 208 q^{67} - 92 q^{68} - 112 q^{69} - 104 q^{70} - 88 q^{71} - 68 q^{73} - 100 q^{74} - 124 q^{75} - 44 q^{76} - 100 q^{77} - 440 q^{78} - 48 q^{79} - 112 q^{80} - 140 q^{82} + 256 q^{83} - 360 q^{84} - 100 q^{85} - 104 q^{86} - 88 q^{87} - 160 q^{88} + 96 q^{90} - 112 q^{91} - 316 q^{92} - 128 q^{93} + 104 q^{94} + 4 q^{95} - 336 q^{96} - 56 q^{97} - 80 q^{99} + O(q^{100}) \)

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

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