Properties

Label 570.6.q
Level $570$
Weight $6$
Character orbit 570.q
Rep. character $\chi_{570}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $200$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1216 200 1016
Cusp forms 1184 200 984
Eisenstein series 32 0 32

Trace form

\( 200 q + 1600 q^{4} + 44 q^{5} + 8100 q^{9} + O(q^{10}) \) \( 200 q + 1600 q^{4} + 44 q^{5} + 8100 q^{9} - 1224 q^{11} - 880 q^{14} - 396 q^{15} - 25600 q^{16} + 2948 q^{19} + 1408 q^{20} - 3168 q^{21} + 3372 q^{25} + 3520 q^{26} + 11344 q^{29} - 8352 q^{30} - 19120 q^{31} + 18496 q^{34} + 12656 q^{35} - 129600 q^{36} + 22320 q^{39} - 4820 q^{41} - 9792 q^{44} + 7128 q^{45} + 37664 q^{46} - 445136 q^{49} + 53760 q^{50} - 20808 q^{51} - 50880 q^{55} - 28160 q^{56} - 5448 q^{59} + 6336 q^{60} - 119872 q^{61} - 819200 q^{64} + 201992 q^{65} - 11376 q^{69} - 12848 q^{70} - 21952 q^{71} + 74160 q^{74} - 96624 q^{75} + 145792 q^{76} - 42976 q^{79} + 11264 q^{80} - 656100 q^{81} - 101376 q^{84} + 201096 q^{85} + 40160 q^{86} - 313844 q^{89} - 539776 q^{91} - 791872 q^{94} - 35012 q^{95} - 49572 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)