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Properties

Label 546.8.o
Level $546$
Weight $8$
Character orbit 546.o
Rep. character $\chi_{546}(265,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $256$
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.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 1584 256 1328
Cusp forms 1552 256 1296
Eisenstein series 32 0 32

Trace form

\( 256 q - 228 q^{7} - 186624 q^{9} + O(q^{10}) \) \( 256 q - 228 q^{7} - 186624 q^{9} - 12112 q^{11} - 7232 q^{14} - 1048576 q^{16} - 122148 q^{21} + 32128 q^{22} - 14592 q^{28} + 959712 q^{29} - 926000 q^{35} - 1423208 q^{37} - 599832 q^{39} - 775168 q^{44} - 1246656 q^{46} - 2205952 q^{50} - 4855744 q^{53} - 4653288 q^{57} - 5106752 q^{58} + 166212 q^{63} + 5663360 q^{65} - 8409520 q^{67} + 4378304 q^{70} - 9601264 q^{71} - 5569792 q^{74} + 2552256 q^{78} + 9941648 q^{79} + 136048896 q^{81} - 7817472 q^{84} + 21235280 q^{85} - 23049344 q^{86} - 25155348 q^{91} + 9325568 q^{92} + 33613272 q^{93} - 11531904 q^{98} + 8829648 q^{99} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)