Properties

Label 462.8.p
Level $462$
Weight $8$
Character orbit 462.p
Rep. character $\chi_{462}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1360 224 1136
Cusp forms 1328 224 1104
Eisenstein series 32 0 32

Trace form

\( 224 q + 7168 q^{4} + 24 q^{5} + 81648 q^{9} + O(q^{10}) \) \( 224 q + 7168 q^{4} + 24 q^{5} + 81648 q^{9} + 4696 q^{11} + 25216 q^{14} + 42552 q^{15} - 458752 q^{16} - 42592 q^{22} - 106184 q^{23} + 1875996 q^{25} - 679872 q^{26} - 38292 q^{31} + 192618 q^{33} + 10450944 q^{36} - 98204 q^{37} + 2123328 q^{38} + 977184 q^{42} - 300544 q^{44} + 17496 q^{45} - 3846576 q^{47} + 6264652 q^{49} + 1664880 q^{53} + 1839104 q^{56} + 537600 q^{58} + 1361664 q^{60} - 58720256 q^{64} - 589344 q^{67} - 13986144 q^{70} + 3457616 q^{71} - 8490744 q^{75} + 44917300 q^{77} - 98304 q^{80} - 59521392 q^{81} - 5260608 q^{82} - 12037056 q^{86} - 1362944 q^{88} - 23911848 q^{89} - 23050512 q^{91} - 13591552 q^{92} - 10050696 q^{93} + 6846768 q^{99} + O(q^{100}) \)

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

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