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Properties

Label 1340.2.bq
Level $1340$
Weight $2$
Character orbit 1340.bq
Rep. character $\chi_{1340}(49,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $680$
Sturm bound $408$

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Defining parameters

Level: \( N \) \(=\) \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1340.bq (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 335 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(408\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1340, [\chi])\).

Total New Old
Modular forms 4200 680 3520
Cusp forms 3960 680 3280
Eisenstein series 240 0 240

Trace form

\( 680 q + 2 q^{5} + 72 q^{9} + O(q^{10}) \) \( 680 q + 2 q^{5} + 72 q^{9} - 4 q^{11} - 12 q^{15} + 32 q^{19} - 16 q^{21} - 2 q^{25} + 6 q^{29} - 54 q^{31} + 7 q^{35} - 12 q^{39} - 88 q^{41} + 20 q^{45} - 26 q^{49} + 10 q^{51} - 76 q^{55} + 58 q^{59} + 122 q^{61} - 98 q^{65} + 56 q^{69} + 156 q^{71} + 66 q^{75} + 98 q^{79} + 128 q^{81} + 20 q^{85} + 110 q^{89} + 20 q^{91} - 44 q^{95} + 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1340, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 2}\)