Properties

Label 570.6.bh
Level $570$
Weight $6$
Character orbit 570.bh
Rep. character $\chi_{570}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1200$
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.bh (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 7296 1200 6096
Cusp forms 7104 1200 5904
Eisenstein series 192 0 192

Trace form

\( 1200 q - 1416 q^{7} + O(q^{10}) \) \( 1200 q - 1416 q^{7} - 4320 q^{21} - 5664 q^{22} - 22128 q^{23} - 7656 q^{25} - 5280 q^{26} - 8856 q^{33} + 28920 q^{41} - 122760 q^{43} + 79728 q^{47} - 190872 q^{53} + 259272 q^{55} - 15336 q^{57} + 38016 q^{60} - 65040 q^{61} - 190272 q^{62} + 59664 q^{67} + 73344 q^{68} + 103488 q^{70} - 421128 q^{73} + 151680 q^{76} - 848160 q^{77} + 50112 q^{78} + 764544 q^{82} + 827472 q^{83} + 887376 q^{85} + 481920 q^{86} - 222696 q^{87} - 984960 q^{91} - 708096 q^{92} - 2297328 q^{95} - 451392 q^{97} - 989952 q^{98} + O(q^{100}) \)

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

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