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Properties

Label 1343.2.k
Level $1343$
Weight $2$
Character orbit 1343.k
Rep. character $\chi_{1343}(712,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $464$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1343 = 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1343.k (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 488 464 24
Cusp forms 472 464 8
Eisenstein series 16 0 16

Trace form

\( 464 q - 8 q^{5} - 24 q^{9} + O(q^{10}) \) \( 464 q - 8 q^{5} - 24 q^{9} - 16 q^{10} + 24 q^{12} - 16 q^{14} - 440 q^{16} - 8 q^{17} - 24 q^{18} + 8 q^{19} + 16 q^{20} - 32 q^{22} - 24 q^{23} + 24 q^{24} + 16 q^{26} - 24 q^{27} + 16 q^{28} - 16 q^{31} - 16 q^{33} - 56 q^{36} - 40 q^{37} - 32 q^{39} + 8 q^{40} + 96 q^{42} + 8 q^{43} + 32 q^{44} - 8 q^{45} - 56 q^{49} - 24 q^{50} + 32 q^{51} + 16 q^{52} + 8 q^{53} + 8 q^{54} - 56 q^{56} + 72 q^{57} + 24 q^{58} - 40 q^{59} + 56 q^{61} + 104 q^{62} - 56 q^{63} + 24 q^{65} - 8 q^{66} - 32 q^{67} - 48 q^{68} + 16 q^{69} - 32 q^{70} - 48 q^{71} + 80 q^{73} - 48 q^{74} - 56 q^{75} - 40 q^{76} - 24 q^{77} - 48 q^{78} + 72 q^{80} - 56 q^{82} + 40 q^{83} - 16 q^{85} + 16 q^{86} - 40 q^{87} + 88 q^{88} + 120 q^{90} - 32 q^{91} + 160 q^{92} - 96 q^{93} + 40 q^{94} - 8 q^{95} - 200 q^{96} - 120 q^{97} + 56 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1343, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)