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Properties

Label 1560.2.ba
Level $1560$
Weight $2$
Character orbit 1560.ba
Rep. character $\chi_{1560}(1091,\cdot)$
Character field $\Q$
Dimension $224$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.ba (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 312 \)
Character field: \(\Q\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 344 224 120
Cusp forms 328 224 104
Eisenstein series 16 0 16

Trace form

\( 224 q + O(q^{10}) \) \( 224 q + 12 q^{12} - 24 q^{22} - 224 q^{25} + 48 q^{27} - 16 q^{30} + 16 q^{36} + 20 q^{42} - 8 q^{48} + 192 q^{49} + 32 q^{52} + 96 q^{64} + 48 q^{66} + 8 q^{78} - 112 q^{82} - 8 q^{88} - 36 q^{90} + 48 q^{91} + 48 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \)