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Properties

Label 570.6.bb
Level $570$
Weight $6$
Character orbit 570.bb
Rep. character $\chi_{570}(41,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $792$
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.bb (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 3648 792 2856
Cusp forms 3552 792 2760
Eisenstein series 96 0 96

Trace form

\( 792 q + 66 q^{3} - 24 q^{6} - 66 q^{9} + O(q^{10}) \) \( 792 q + 66 q^{3} - 24 q^{6} - 66 q^{9} - 12888 q^{13} + 72 q^{19} - 22752 q^{22} - 384 q^{24} + 47322 q^{27} + 8064 q^{28} - 34530 q^{33} + 18336 q^{34} - 1056 q^{36} + 9528 q^{39} - 154608 q^{43} + 33792 q^{48} - 893172 q^{49} + 84498 q^{51} - 42624 q^{52} - 164448 q^{54} - 268644 q^{57} - 128832 q^{58} - 309168 q^{61} + 277536 q^{63} - 1622016 q^{64} + 60600 q^{66} + 247548 q^{67} + 179388 q^{69} - 185088 q^{72} - 209088 q^{73} - 263376 q^{78} - 299448 q^{79} - 577434 q^{81} - 261168 q^{82} + 266268 q^{87} + 213600 q^{90} + 97776 q^{91} + 327324 q^{97} - 133680 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)