↑

Properties

Label 308.1.s
Level $308$
Weight $1$
Character orbit 308.s
Rep. character $\chi_{308}(83,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $8$
Newform subspaces $2$
Sturm bound $48$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 308.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 308 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(308, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 2 q^{4} + 2 q^{9} - 3 q^{14} - 2 q^{16} - 5 q^{18} + 2 q^{22} - 2 q^{25} - 5 q^{28} + 2 q^{36} - 6 q^{37} + 5 q^{44} + 5 q^{46} - 2 q^{49} - 6 q^{53} + 2 q^{56} + 5 q^{58} - 2 q^{64} + 5 q^{72} - 2 q^{77}+ \cdots + 5 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(308, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
308.1.s.a 308.s 308.s $4$ $0.154$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-7}) \) None 308.1.s.a \(-1\) \(0\) \(0\) \(1\) \(q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots\)
308.1.s.b 308.s 308.s $4$ $0.154$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-7}) \) None 308.1.s.a \(1\) \(0\) \(0\) \(-1\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots\)