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Properties

Label 3415.1.d
Level $3415$
Weight $1$
Character orbit 3415.d
Rep. character $\chi_{3415}(3414,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $2$
Sturm bound $342$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3415 = 5 \cdot 683 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3415.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3415 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(342\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3415, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 18 18 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 18 0 0 0

Trace form

\( 18 q + 16 q^{4} + 18 q^{9} + O(q^{10}) \) \( 18 q + 16 q^{4} + 18 q^{9} - 2 q^{10} - 4 q^{14} + 14 q^{16} - 2 q^{19} + 18 q^{25} - 4 q^{26} - 2 q^{29} - 4 q^{34} - 2 q^{35} + 16 q^{36} - 4 q^{40} - 4 q^{46} + 16 q^{49} - 8 q^{56} - 2 q^{59} - 2 q^{61} + 12 q^{64} - 2 q^{65} - 2 q^{71} - 4 q^{74} - 6 q^{76} + 18 q^{81} - 2 q^{85} - 4 q^{86} - 2 q^{90} - 4 q^{91} - 4 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3415, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3415.1.d.a 3415.d 3415.d $9$ $1.704$ \(\Q(\zeta_{38})^+\) $D_{19}$ \(\Q(\sqrt{-3415}) \) None \(-1\) \(0\) \(9\) \(-1\) \(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
3415.1.d.b 3415.d 3415.d $9$ $1.704$ \(\Q(\zeta_{38})^+\) $D_{19}$ \(\Q(\sqrt{-3415}) \) None \(1\) \(0\) \(-9\) \(1\) \(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)