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Properties

Label 462.6.j
Level $462$
Weight $6$
Character orbit 462.j
Rep. character $\chi_{462}(169,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $240$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 462.j (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1952 240 1712
Cusp forms 1888 240 1648
Eisenstein series 64 0 64

Trace form

\( 240 q - 960 q^{4} - 4860 q^{9} + O(q^{10}) \) \( 240 q - 960 q^{4} - 4860 q^{9} + 2848 q^{11} - 4520 q^{13} + 1584 q^{15} - 15360 q^{16} + 5776 q^{17} + 7024 q^{19} + 7056 q^{21} - 944 q^{22} + 15824 q^{23} - 56904 q^{25} + 2528 q^{26} + 1152 q^{30} + 20080 q^{31} + 720 q^{33} + 3520 q^{34} - 77760 q^{36} - 5632 q^{37} + 14048 q^{38} + 22320 q^{39} - 23024 q^{41} + 148688 q^{43} - 11392 q^{44} - 83264 q^{46} - 33008 q^{47} - 144060 q^{49} + 17088 q^{50} + 30888 q^{51} + 76160 q^{52} + 118888 q^{53} + 24168 q^{55} + 65088 q^{57} - 35296 q^{58} + 37048 q^{59} - 38016 q^{60} + 93000 q^{61} - 190272 q^{62} - 245760 q^{64} + 11600 q^{65} - 97632 q^{66} - 83424 q^{67} + 92416 q^{68} + 211464 q^{69} - 17248 q^{70} + 202984 q^{71} + 220504 q^{73} + 193248 q^{75} + 112384 q^{76} + 47824 q^{77} + 71336 q^{79} - 393660 q^{81} + 380864 q^{82} + 117568 q^{83} - 28224 q^{84} - 415676 q^{85} - 259232 q^{86} + 156960 q^{87} - 15104 q^{88} + 94848 q^{89} + 81024 q^{92} + 171468 q^{93} - 34240 q^{94} + 449888 q^{95} + 575712 q^{97} - 57672 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{6}^{\mathrm{old}}(462, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)