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Properties

Label 570.6.bi
Level $570$
Weight $6$
Character orbit 570.bi
Rep. character $\chi_{570}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2400$
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.bi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 7296 2400 4896
Cusp forms 7104 2400 4704
Eisenstein series 192 0 192

Trace form

\( 2400 q + O(q^{10}) \) \( 2400 q - 6516 q^{15} + 13632 q^{18} + 5664 q^{22} + 7656 q^{25} - 17208 q^{33} + 21144 q^{43} - 11916 q^{45} + 264120 q^{51} - 290040 q^{55} - 336492 q^{57} - 46848 q^{60} - 65040 q^{61} - 43236 q^{63} + 475680 q^{66} - 205392 q^{67} - 103488 q^{70} - 562368 q^{78} + 805680 q^{81} + 431472 q^{85} + 270624 q^{87} - 176928 q^{90} - 1311120 q^{91} - 1827588 q^{93} - 538032 q^{97} + O(q^{100}) \)

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

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