↑

Properties

Label 608.4.bh
Level $608$
Weight $4$
Character orbit 608.bh
Rep. character $\chi_{608}(15,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $348$
Sturm bound $320$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 608.bh (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

\( 348 q + 12 q^{3} - 12 q^{9} + O(q^{10}) \) \( 348 q + 12 q^{3} - 12 q^{9} + 6 q^{11} - 12 q^{17} + 12 q^{19} - 12 q^{25} + 18 q^{27} + 150 q^{33} + 762 q^{35} + 48 q^{41} + 12 q^{43} + 6756 q^{49} - 2220 q^{51} - 12 q^{57} + 12 q^{59} - 18 q^{65} + 12 q^{67} - 660 q^{73} + 1206 q^{81} + 6 q^{83} - 12 q^{89} + 2070 q^{91} - 12 q^{97} - 4362 q^{99} + O(q^{100}) \)

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

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