Properties

Label 1716.2.o
Level $1716$
Weight $2$
Character orbit 1716.o
Rep. character $\chi_{1716}(155,\cdot)$
Character field $\Q$
Dimension $280$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1716.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 156 \)
Character field: \(\Q\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1716, [\chi])\).

Total New Old
Modular forms 344 280 64
Cusp forms 328 280 48
Eisenstein series 16 0 16

Trace form

\( 280 q + O(q^{10}) \) \( 280 q + 12 q^{12} + 8 q^{13} + 280 q^{25} + 2 q^{36} - 40 q^{40} + 10 q^{42} - 74 q^{48} + 328 q^{49} - 56 q^{52} + 16 q^{61} + 48 q^{64} - 10 q^{66} - 34 q^{78} - 32 q^{81} - 32 q^{82} - 24 q^{88} - 48 q^{90} - 72 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1716, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1716, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)