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Properties

Label 462.6.y
Level $462$
Weight $6$
Character orbit 462.y
Rep. character $\chi_{462}(25,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $640$
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.y (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 3904 640 3264
Cusp forms 3776 640 3136
Eisenstein series 128 0 128

Trace form

\( 640 q + 1280 q^{4} + 88 q^{5} + 288 q^{6} - 632 q^{7} + 6480 q^{9} + O(q^{10}) \) \( 640 q + 1280 q^{4} + 88 q^{5} + 288 q^{6} - 632 q^{7} + 6480 q^{9} + 2704 q^{10} - 296 q^{11} + 2704 q^{13} - 2992 q^{14} - 1188 q^{15} + 20480 q^{16} + 7836 q^{17} - 6048 q^{19} - 2816 q^{20} + 5232 q^{22} - 2552 q^{23} - 2304 q^{24} + 56424 q^{25} - 1760 q^{26} - 16928 q^{28} - 15144 q^{29} + 8352 q^{30} - 9966 q^{31} - 2358 q^{33} + 24448 q^{34} + 56296 q^{35} - 207360 q^{36} + 23332 q^{37} + 352 q^{38} - 896 q^{40} + 65832 q^{41} + 14328 q^{42} - 27536 q^{43} + 20544 q^{44} + 7128 q^{45} + 37312 q^{46} - 93448 q^{47} + 63536 q^{49} - 31320 q^{51} - 21632 q^{52} + 13184 q^{53} + 46656 q^{54} + 119068 q^{55} - 61952 q^{56} - 10224 q^{57} - 21160 q^{58} - 70624 q^{59} - 6336 q^{60} - 396484 q^{61} - 428160 q^{62} - 69660 q^{63} - 655360 q^{64} + 315456 q^{65} - 39392 q^{67} + 125376 q^{68} + 208728 q^{69} + 148344 q^{70} - 264528 q^{71} - 251448 q^{73} + 2944 q^{74} - 9432 q^{75} - 268544 q^{76} - 1074656 q^{77} - 305360 q^{79} - 33792 q^{80} + 524880 q^{81} + 5280 q^{82} + 218416 q^{83} + 464944 q^{85} + 302544 q^{86} + 111924 q^{87} + 148864 q^{88} + 423824 q^{89} + 209952 q^{90} + 626892 q^{91} + 81664 q^{92} + 98316 q^{93} - 607040 q^{94} + 161508 q^{95} - 36864 q^{96} - 639768 q^{97} - 8256 q^{98} + 47952 q^{99} + O(q^{100}) \)

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

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