↑

Properties

Label 570.6.u
Level $570$
Weight $6$
Character orbit 570.u
Rep. character $\chi_{570}(61,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $408$
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.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 3648 408 3240
Cusp forms 3552 408 3144
Eisenstein series 96 0 96

Trace form

\( 408 q + O(q^{10}) \) \( 408 q - 4200 q^{13} - 5280 q^{14} + 17976 q^{17} - 672 q^{19} - 5832 q^{21} + 14304 q^{22} - 27408 q^{23} - 2640 q^{26} + 19200 q^{28} - 30288 q^{29} - 26184 q^{31} - 18336 q^{34} - 8700 q^{35} + 72960 q^{37} + 42144 q^{38} - 15948 q^{41} + 35424 q^{42} + 99144 q^{43} - 960 q^{44} - 85704 q^{47} - 500172 q^{49} - 26880 q^{52} - 52536 q^{53} - 33792 q^{56} + 128832 q^{58} - 51096 q^{59} + 68280 q^{61} - 139296 q^{62} - 77760 q^{63} - 835584 q^{64} - 63300 q^{65} - 365328 q^{67} + 49656 q^{71} + 374064 q^{73} - 222480 q^{74} + 75840 q^{76} - 820656 q^{77} - 19944 q^{79} - 73056 q^{82} - 118824 q^{83} - 292032 q^{86} - 185856 q^{88} - 452640 q^{89} - 253896 q^{91} + 219264 q^{92} - 39528 q^{93} - 109920 q^{94} + 563328 q^{97} - 405312 q^{98} - 4860 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)