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Properties

Label 1666.2.bc
Level $1666$
Weight $2$
Character orbit 1666.bc
Rep. character $\chi_{1666}(31,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $960$
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.bc (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 4288 960 3328
Cusp forms 3776 960 2816
Eisenstein series 512 0 512

Trace form

\( 960 q + O(q^{10}) \) \( 960 q + 16 q^{11} + 96 q^{15} + 32 q^{18} + 32 q^{22} + 16 q^{25} + 32 q^{37} - 64 q^{39} + 64 q^{44} - 64 q^{46} + 128 q^{51} - 128 q^{53} + 64 q^{58} - 64 q^{60} + 48 q^{61} + 64 q^{65} - 64 q^{71} + 240 q^{73} - 96 q^{74} + 144 q^{75} - 128 q^{78} + 48 q^{80} + 192 q^{81} - 64 q^{85} + 288 q^{87} + 64 q^{88} - 32 q^{92} - 128 q^{93} + 192 q^{94} + 128 q^{95} - 672 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 2}\)