↑

Properties

Label 3311.1.ex
Level $3311$
Weight $1$
Character orbit 3311.ex
Rep. character $\chi_{3311}(118,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $48$
Newform subspaces $2$
Sturm bound $352$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3311 = 7 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3311.ex (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3311 \)
Character field: \(\Q(\zeta_{70})\)
Newform subspaces: \( 2 \)
Sturm bound: \(352\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3311, [\chi])\).

Total New Old
Modular forms 144 144 0
Cusp forms 48 48 0
Eisenstein series 96 96 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 48 0 0 0

Trace form

\( 48 q + 6 q^{4} + 35 q^{8} - 2 q^{9} + O(q^{10}) \) \( 48 q + 6 q^{4} + 35 q^{8} - 2 q^{9} - 2 q^{11} - 6 q^{14} - 4 q^{23} - 2 q^{25} + 8 q^{36} - 52 q^{44} - 12 q^{49} + 15 q^{53} - 6 q^{56} + 16 q^{58} + 25 q^{64} + 4 q^{67} - 10 q^{79} + 2 q^{81} - 20 q^{86} - 7 q^{88} + 8 q^{92} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3311, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3311.1.ex.a 3311.ex 3311.dx $24$ $1.652$ \(\Q(\zeta_{35})\) $D_{70}$ \(\Q(\sqrt{-7}) \) None 3311.1.ex.a \(-2\) \(0\) \(0\) \(6\) \(q+(\zeta_{70}^{23}+\zeta_{70}^{31})q^{2}+(-\zeta_{70}^{11}+\cdots)q^{4}+\cdots\)
3311.1.ex.b 3311.ex 3311.dx $24$ $1.652$ \(\Q(\zeta_{35})\) $D_{70}$ \(\Q(\sqrt{-7}) \) None 3311.1.ex.a \(2\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{70}^{3}+\zeta_{70}^{16})q^{2}+(\zeta_{70}^{6}-\zeta_{70}^{19}+\cdots)q^{4}+\cdots\)