Properties

Label 462.4.y
Level $462$
Weight $4$
Character orbit 462.y
Rep. character $\chi_{462}(25,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $384$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 462.y (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 2368 384 1984
Cusp forms 2240 384 1856
Eisenstein series 128 0 128

Trace form

\( 384 q + 192 q^{4} - 32 q^{5} - 48 q^{6} + 36 q^{7} + 432 q^{9} + O(q^{10}) \) \( 384 q + 192 q^{4} - 32 q^{5} - 48 q^{6} + 36 q^{7} + 432 q^{9} - 296 q^{10} + 28 q^{11} - 208 q^{13} + 104 q^{14} + 252 q^{15} + 768 q^{16} + 780 q^{17} + 288 q^{19} + 256 q^{20} - 424 q^{22} - 56 q^{23} + 96 q^{24} + 1456 q^{25} + 304 q^{26} + 56 q^{28} + 840 q^{29} - 48 q^{30} - 414 q^{31} + 6 q^{33} - 960 q^{34} - 3536 q^{35} - 3456 q^{36} - 972 q^{37} + 496 q^{38} + 176 q^{40} - 120 q^{41} + 564 q^{42} + 672 q^{43} - 1008 q^{44} - 288 q^{45} + 352 q^{46} + 752 q^{47} - 2036 q^{49} + 1008 q^{51} + 416 q^{52} - 616 q^{53} - 864 q^{54} + 3940 q^{55} + 448 q^{56} + 1392 q^{57} + 420 q^{58} - 2032 q^{59} + 336 q^{60} - 1280 q^{61} - 3648 q^{62} - 6144 q^{64} - 4224 q^{65} + 3424 q^{67} + 3120 q^{68} - 984 q^{69} + 3948 q^{70} + 7776 q^{71} + 5332 q^{73} + 3136 q^{74} - 312 q^{75} + 3776 q^{76} + 9400 q^{77} + 3276 q^{79} + 768 q^{80} + 3888 q^{81} + 48 q^{82} + 4912 q^{83} + 7864 q^{85} - 504 q^{86} + 948 q^{87} - 272 q^{88} - 2752 q^{89} - 1872 q^{90} - 6372 q^{91} + 448 q^{92} - 2028 q^{93} + 1184 q^{94} - 6936 q^{95} + 384 q^{96} + 5928 q^{97} + 2592 q^{98} - 504 q^{99} + O(q^{100}) \)

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

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