Properties

Label 1666.2.t
Level $1666$
Weight $2$
Character orbit 1666.t
Rep. character $\chi_{1666}(97,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $480$
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.t (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 2144 480 1664
Cusp forms 1888 480 1408
Eisenstein series 256 0 256

Trace form

\( 480 q + O(q^{10}) \) \( 480 q + 32 q^{11} - 96 q^{15} + 64 q^{18} - 32 q^{22} + 32 q^{25} + 64 q^{37} + 64 q^{39} - 64 q^{44} + 64 q^{46} - 128 q^{51} + 128 q^{53} - 64 q^{58} + 64 q^{60} - 64 q^{65} + 64 q^{71} + 96 q^{74} + 128 q^{78} - 192 q^{81} + 256 q^{85} - 64 q^{88} + 32 q^{92} + 128 q^{93} - 128 q^{95} - 96 q^{99} + O(q^{100}) \)

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

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