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Properties

Label 570.4.u
Level $570$
Weight $4$
Character orbit 570.u
Rep. character $\chi_{570}(61,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $240$
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.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2208 240 1968
Cusp forms 2112 240 1872
Eisenstein series 96 0 96

Trace form

\( 240 q + O(q^{10}) \) \( 240 q + 144 q^{12} - 12 q^{13} + 48 q^{14} - 744 q^{17} - 444 q^{19} - 396 q^{21} - 336 q^{22} + 96 q^{23} + 456 q^{26} + 324 q^{27} + 528 q^{28} + 1680 q^{29} + 120 q^{31} + 720 q^{34} - 780 q^{35} - 768 q^{37} - 624 q^{38} - 756 q^{41} + 144 q^{42} + 1428 q^{43} + 336 q^{44} + 768 q^{47} - 3600 q^{49} - 1056 q^{52} + 1176 q^{53} + 1920 q^{56} - 2592 q^{58} - 2640 q^{59} + 1488 q^{61} - 3216 q^{62} + 216 q^{63} - 7680 q^{64} + 420 q^{65} + 2436 q^{67} - 5640 q^{71} + 12 q^{73} - 792 q^{74} - 1800 q^{75} - 816 q^{76} + 10944 q^{77} - 1032 q^{79} + 1584 q^{82} - 456 q^{83} - 7776 q^{86} + 2112 q^{88} + 2688 q^{89} - 4416 q^{91} - 192 q^{92} + 2520 q^{93} + 1872 q^{94} + 10248 q^{97} + 4512 q^{98} + 756 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)