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Properties

Label 1342.2.cx
Level $1342$
Weight $2$
Character orbit 1342.cx
Rep. character $\chi_{1342}(35,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $992$
Sturm bound $372$

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Defining parameters

Level: \( N \) \(=\) \( 1342 = 2 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1342.cx (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 671 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(372\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1342, [\chi])\).

Total New Old
Modular forms 3040 992 2048
Cusp forms 2912 992 1920
Eisenstein series 128 0 128

Trace form

\( 992 q + 248 q^{9} + O(q^{10}) \) \( 992 q + 248 q^{9} + 4 q^{11} - 124 q^{16} - 16 q^{20} + 64 q^{23} - 96 q^{25} - 4 q^{26} - 60 q^{29} - 12 q^{31} - 28 q^{33} - 32 q^{37} + 12 q^{38} + 8 q^{44} - 120 q^{45} + 64 q^{47} - 136 q^{49} + 60 q^{53} + 20 q^{55} - 28 q^{56} - 80 q^{57} + 56 q^{58} + 32 q^{59} + 80 q^{61} + 80 q^{65} - 8 q^{66} - 56 q^{67} - 40 q^{68} + 104 q^{69} - 48 q^{70} + 20 q^{71} + 80 q^{74} - 44 q^{77} - 168 q^{78} - 216 q^{81} + 64 q^{82} + 120 q^{84} + 40 q^{85} - 40 q^{86} - 12 q^{89} + 20 q^{90} + 88 q^{91} + 16 q^{92} - 140 q^{93} + 96 q^{97} + 120 q^{98} + 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1342, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1342, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1342, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(671, [\chi])\)\(^{\oplus 2}\)