↑

Properties

Label 608.2.u
Level $608$
Weight $2$
Character orbit 608.u
Rep. character $\chi_{608}(75,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $312$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 608.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 608 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(608, [\chi])\).

Total New Old
Modular forms 328 328 0
Cusp forms 312 312 0
Eisenstein series 16 16 0

Trace form

\( 312 q - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 312 q - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{9} - 8 q^{11} - 8 q^{16} - 4 q^{19} - 8 q^{20} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 48 q^{26} + 32 q^{28} + 8 q^{30} - 56 q^{35} - 8 q^{36} - 52 q^{38} - 8 q^{39} - 88 q^{42} - 8 q^{43} + 80 q^{44} + 16 q^{45} - 16 q^{47} - 32 q^{54} - 8 q^{55} - 4 q^{57} - 8 q^{58} - 72 q^{61} - 48 q^{62} - 80 q^{64} - 120 q^{66} - 8 q^{68} - 8 q^{73} - 8 q^{74} + 60 q^{76} - 8 q^{77} + 128 q^{80} - 88 q^{82} - 8 q^{83} + 32 q^{85} + 104 q^{87} - 8 q^{92} - 32 q^{93} + 96 q^{96} - 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
608.2.u.a 608.u 608.u $312$ $4.855$ None \(0\) \(0\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{8}]$