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Properties

Label 1666.2.bn
Level $1666$
Weight $2$
Character orbit 1666.bn
Rep. character $\chi_{1666}(3,\cdot)$
Character field $\Q(\zeta_{336})$
Dimension $8064$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1666.bn (of order \(336\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 833 \)
Character field: \(\Q(\zeta_{336})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1666, [\chi])\).

Total New Old
Modular forms 24576 8064 16512
Cusp forms 23808 8064 15744
Eisenstein series 768 0 768

Trace form

\( 8064 q + O(q^{10}) \) \( 8064 q + 128 q^{11} - 16 q^{14} + 96 q^{15} + 32 q^{18} - 48 q^{21} + 32 q^{22} + 16 q^{25} + 32 q^{35} + 32 q^{37} + 96 q^{42} - 768 q^{49} + 48 q^{61} + 48 q^{63} + 224 q^{69} - 64 q^{71} + 240 q^{73} - 192 q^{75} - 16 q^{77} + 320 q^{78} + 48 q^{80} - 192 q^{85} + 288 q^{87} + 64 q^{91} - 32 q^{92} + 192 q^{94} - 160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1666, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)