Properties

Label 462.6.k
Level $462$
Weight $6$
Character orbit 462.k
Rep. character $\chi_{462}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $264$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 462.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(462, [\chi])\).

Total New Old
Modular forms 976 264 712
Cusp forms 944 264 680
Eisenstein series 32 0 32

Trace form

\( 264 q + 2112 q^{4} + 384 q^{7} - 380 q^{9} + O(q^{10}) \) \( 264 q + 2112 q^{4} + 384 q^{7} - 380 q^{9} - 3368 q^{15} - 33792 q^{16} - 2272 q^{18} - 5304 q^{19} - 2888 q^{21} + 3840 q^{24} - 77500 q^{25} + 8832 q^{28} - 4896 q^{30} - 24984 q^{31} - 12160 q^{36} + 1532 q^{37} - 11396 q^{39} - 52848 q^{42} - 29440 q^{43} - 5784 q^{45} + 36608 q^{46} - 102768 q^{49} + 71572 q^{51} + 82944 q^{52} + 120816 q^{54} + 123992 q^{57} - 45552 q^{58} - 26944 q^{60} - 596400 q^{61} - 138152 q^{63} - 1081344 q^{64} - 139904 q^{67} - 95552 q^{70} + 36352 q^{72} + 228408 q^{73} + 168444 q^{75} - 104832 q^{78} - 321776 q^{79} + 194140 q^{81} - 118176 q^{82} + 143168 q^{84} + 494576 q^{85} - 563796 q^{87} - 446384 q^{91} + 599660 q^{93} + 449472 q^{94} + 61440 q^{96} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)