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Properties

Label 462.6.u
Level $462$
Weight $6$
Character orbit 462.u
Rep. character $\chi_{462}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
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.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1952 320 1632
Cusp forms 1888 320 1568
Eisenstein series 64 0 64

Trace form

\( 320 q + 1280 q^{4} + 1180 q^{7} + 6480 q^{9} + O(q^{10}) \) \( 320 q + 1280 q^{4} + 1180 q^{7} + 6480 q^{9} - 592 q^{11} + 2992 q^{14} - 1188 q^{15} - 20480 q^{16} + 5248 q^{22} - 5104 q^{23} + 68876 q^{25} - 3040 q^{28} - 25240 q^{29} - 27980 q^{35} - 103680 q^{36} - 35968 q^{37} - 20232 q^{42} - 41088 q^{44} - 2592 q^{49} + 104400 q^{51} + 43680 q^{53} + 22528 q^{56} - 22256 q^{58} - 12672 q^{60} + 95580 q^{63} + 327680 q^{64} + 483296 q^{67} - 83096 q^{70} - 248160 q^{71} - 368320 q^{74} - 25736 q^{77} - 502680 q^{79} - 524880 q^{81} + 381580 q^{85} + 605088 q^{86} + 297472 q^{88} + 713216 q^{91} + 81664 q^{92} - 200196 q^{93} - 1458440 q^{95} + 47952 q^{99} + O(q^{100}) \)

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

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