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Properties

Label 546.8.g
Level $546$
Weight $8$
Character orbit 546.g
Rep. character $\chi_{546}(209,\cdot)$
Character field $\Q$
Dimension $224$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 546.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(546, [\chi])\).

Total New Old
Modular forms 792 224 568
Cusp forms 776 224 552
Eisenstein series 16 0 16

Trace form

\( 224 q - 14336 q^{4} - 1348 q^{7} - 3016 q^{9} + O(q^{10}) \) \( 224 q - 14336 q^{4} - 1348 q^{7} - 3016 q^{9} - 50376 q^{15} + 917504 q^{16} - 34624 q^{21} - 99840 q^{22} + 3611280 q^{25} + 86272 q^{28} + 197152 q^{30} + 193024 q^{36} - 435528 q^{37} - 529136 q^{42} + 4392128 q^{43} - 1386176 q^{46} + 3838012 q^{49} + 8290652 q^{51} - 9013664 q^{57} - 4457920 q^{58} + 3224064 q^{60} - 8678900 q^{63} - 58720256 q^{64} - 8515968 q^{70} + 17308104 q^{79} + 11110648 q^{81} + 2215936 q^{84} - 39531008 q^{85} + 6389760 q^{88} + 4200664 q^{91} - 151912 q^{93} - 99687168 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)