Properties

Label 2240.2.dx
Level $2240$
Weight $2$
Character orbit 2240.dx
Rep. character $\chi_{2240}(141,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1536$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.dx (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2240, [\chi])\).

Total New Old
Modular forms 3104 1536 1568
Cusp forms 3040 1536 1504
Eisenstein series 64 0 64

Trace form

\( 1536q + O(q^{10}) \) \( 1536q + 16q^{22} + 160q^{32} + 160q^{34} + 16q^{44} + 64q^{51} - 128q^{54} - 16q^{56} - 288q^{58} - 192q^{62} + 160q^{63} + 160q^{67} - 192q^{68} - 288q^{72} - 16q^{74} - 128q^{76} + 96q^{78} + 64q^{79} + 128q^{80} + 416q^{86} + 320q^{88} + 32q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)