Properties

Label 608.4.t
Level $608$
Weight $4$
Character orbit 608.t
Rep. character $\chi_{608}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
Sturm bound $320$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 496 124 372
Cusp forms 464 116 348
Eisenstein series 32 8 24

Trace form

\( 116q + 8q^{7} + 484q^{9} + O(q^{10}) \) \( 116q + 8q^{7} + 484q^{9} + 230q^{15} - 2q^{17} + 2q^{23} + 1248q^{25} - 208q^{31} - 180q^{33} + 116q^{39} - 22q^{41} - 202q^{47} + 5220q^{49} - 248q^{55} - 398q^{57} + 796q^{63} - 508q^{65} - 1986q^{71} - 218q^{73} - 1250q^{79} - 3810q^{81} + 1404q^{87} - 2q^{89} - 438q^{95} - 1586q^{97} + O(q^{100}) \)

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

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