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Properties

Label 608.4.bf
Level $608$
Weight $4$
Character orbit 608.bf
Rep. character $\chi_{608}(17,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $348$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 608.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(608, [\chi])\).

Total New Old
Modular forms 1488 372 1116
Cusp forms 1392 348 1044
Eisenstein series 96 24 72

Trace form

\( 348 q + 6 q^{7} - 12 q^{9} + O(q^{10}) \) \( 348 q + 6 q^{7} - 12 q^{9} + 12 q^{15} - 12 q^{17} + 12 q^{23} - 12 q^{25} + 1122 q^{31} - 174 q^{33} + 24 q^{39} + 48 q^{41} + 624 q^{47} - 6768 q^{49} + 762 q^{55} - 12 q^{57} - 2046 q^{63} - 6 q^{65} + 12 q^{71} + 636 q^{73} + 12 q^{79} + 1206 q^{81} + 6 q^{87} - 12 q^{89} - 1848 q^{95} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(608, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)