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Properties

Label 462.8.ba
Level $462$
Weight $8$
Character orbit 462.ba
Rep. character $\chi_{462}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $896$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 462.ba (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(462, [\chi])\).

Total New Old
Modular forms 5440 896 4544
Cusp forms 5312 896 4416
Eisenstein series 128 0 128

Trace form

\( 896 q - 7168 q^{4} - 24 q^{5} + 3940 q^{7} - 81648 q^{9} + O(q^{10}) \) \( 896 q - 7168 q^{4} - 24 q^{5} + 3940 q^{7} - 81648 q^{9} - 4696 q^{11} + 19744 q^{14} + 63828 q^{15} + 458752 q^{16} + 310020 q^{17} + 42592 q^{22} + 106184 q^{23} - 1546576 q^{25} + 679872 q^{26} - 215680 q^{28} + 1328840 q^{29} - 57438 q^{31} - 192618 q^{33} - 1085240 q^{35} - 10450944 q^{36} + 98204 q^{37} - 2123328 q^{38} - 199680 q^{40} - 162864 q^{42} - 2171136 q^{44} - 17496 q^{45} + 3846576 q^{47} + 1039488 q^{49} - 484920 q^{51} - 1664880 q^{53} - 1839104 q^{56} + 39280 q^{58} - 1361664 q^{60} - 44782140 q^{61} + 2872260 q^{63} + 58720256 q^{64} - 15919456 q^{67} - 19841280 q^{68} - 12798416 q^{70} - 34175856 q^{71} + 23415660 q^{73} + 11186240 q^{74} + 8490744 q^{75} + 10661200 q^{77} + 11237460 q^{79} - 147456 q^{80} + 59521392 q^{81} - 44696832 q^{82} - 96353360 q^{85} - 18055584 q^{86} + 3933184 q^{88} + 90621168 q^{89} + 137350292 q^{91} + 13591552 q^{92} - 106164 q^{93} - 67119360 q^{94} - 76683620 q^{95} - 6846768 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(462, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(462, [\chi])\) into lower level spaces

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