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Properties

Label 570.4.bh
Level $570$
Weight $4$
Character orbit 570.bh
Rep. character $\chi_{570}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $720$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.bh (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(570, [\chi])\).

Total New Old
Modular forms 4416 720 3696
Cusp forms 4224 720 3504
Eisenstein series 192 0 192

Trace form

\( 720 q + 48 q^{7} + O(q^{10}) \) \( 720 q + 48 q^{7} - 1152 q^{21} + 432 q^{22} + 1056 q^{23} - 216 q^{25} + 912 q^{26} + 1152 q^{33} - 888 q^{41} + 1200 q^{43} - 2064 q^{47} + 3744 q^{53} - 4248 q^{55} + 2088 q^{57} + 576 q^{60} - 5184 q^{61} + 96 q^{62} - 5712 q^{67} + 3072 q^{68} + 6048 q^{70} + 576 q^{73} - 1632 q^{76} - 13680 q^{77} + 2016 q^{78} - 5952 q^{82} + 1416 q^{83} + 2496 q^{85} + 2112 q^{86} + 1368 q^{87} + 9744 q^{91} + 8448 q^{92} + 16032 q^{95} + 9216 q^{97} + 15744 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)