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 $320$

Related objects

Downloads

Learn more

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

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

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

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