↑

Properties

Label 570.4.q
Level $570$
Weight $4$
Character orbit 570.q
Rep. character $\chi_{570}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 736 120 616
Cusp forms 704 120 584
Eisenstein series 32 0 32

Trace form

\( 120 q + 240 q^{4} - 16 q^{5} + 540 q^{9} + O(q^{10}) \) \( 120 q + 240 q^{4} - 16 q^{5} + 540 q^{9} + 168 q^{11} + 8 q^{14} - 24 q^{15} - 960 q^{16} - 308 q^{19} - 128 q^{20} + 264 q^{21} + 228 q^{25} - 608 q^{26} + 64 q^{29} + 48 q^{30} + 288 q^{31} - 544 q^{34} + 92 q^{35} - 2160 q^{36} - 672 q^{39} + 148 q^{41} + 336 q^{44} - 288 q^{45} + 1040 q^{46} - 6544 q^{49} - 768 q^{50} + 408 q^{51} - 1512 q^{55} + 64 q^{56} - 3384 q^{59} + 96 q^{60} - 2752 q^{61} - 7680 q^{64} - 3328 q^{65} + 4704 q^{69} - 440 q^{70} - 2080 q^{71} + 264 q^{74} + 96 q^{75} - 1312 q^{76} - 3184 q^{79} - 256 q^{80} - 4860 q^{81} + 2112 q^{84} + 2760 q^{85} + 176 q^{86} + 4780 q^{89} + 168 q^{91} + 4960 q^{94} - 488 q^{95} + 756 q^{99} + O(q^{100}) \)

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

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