↑

Properties

Label 462.4.u
Level $462$
Weight $4$
Character orbit 462.u
Rep. character $\chi_{462}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 462.u (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(462, [\chi])\).

Total New Old
Modular forms 1184 192 992
Cusp forms 1120 192 928
Eisenstein series 64 0 64

Trace form

\( 192 q + 192 q^{4} - 40 q^{7} + 432 q^{9} + O(q^{10}) \) \( 192 q + 192 q^{4} - 40 q^{7} + 432 q^{9} + 56 q^{11} - 104 q^{14} + 252 q^{15} - 768 q^{16} + 128 q^{22} - 112 q^{23} + 2372 q^{25} - 120 q^{28} + 1400 q^{29} + 580 q^{35} - 1728 q^{36} + 1392 q^{37} - 588 q^{42} + 2016 q^{44} - 1452 q^{49} - 3360 q^{51} - 336 q^{53} + 256 q^{56} - 168 q^{58} + 672 q^{60} - 360 q^{63} + 3072 q^{64} - 3072 q^{67} + 516 q^{70} + 5568 q^{71} + 5600 q^{74} + 6532 q^{77} + 8400 q^{79} - 3888 q^{81} + 2060 q^{85} - 1008 q^{86} - 2752 q^{88} - 2364 q^{91} + 448 q^{92} + 2004 q^{93} - 10640 q^{95} - 504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

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