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Properties

Label 570.6.f
Level $570$
Weight $6$
Character orbit 570.f
Rep. character $\chi_{570}(341,\cdot)$
Character field $\Q$
Dimension $136$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(570, [\chi])\).

Total New Old
Modular forms 608 136 472
Cusp forms 592 136 456
Eisenstein series 16 0 16

Trace form

\( 136 q + 2176 q^{4} + 16 q^{6} + 856 q^{7} + 44 q^{9} + O(q^{10}) \) \( 136 q + 2176 q^{4} + 16 q^{6} + 856 q^{7} + 44 q^{9} + 34816 q^{16} + 2984 q^{19} + 256 q^{24} - 85000 q^{25} + 13696 q^{28} + 704 q^{36} + 78772 q^{39} + 48 q^{42} + 8976 q^{43} + 11600 q^{45} + 201264 q^{49} - 92768 q^{54} - 134836 q^{57} + 43104 q^{58} + 247872 q^{61} + 156924 q^{63} + 557056 q^{64} + 36416 q^{66} + 293416 q^{73} + 47744 q^{76} + 200700 q^{81} + 160320 q^{82} - 463596 q^{87} + 276176 q^{93} + 4096 q^{96} + 339968 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(570, [\chi]) \cong \)