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Properties

Label 2940.1.dd
Level $2940$
Weight $1$
Character orbit 2940.dd
Rep. character $\chi_{2940}(59,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $48$
Newform subspaces $2$
Sturm bound $672$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2940.dd (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2940 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 2 \)
Sturm bound: \(672\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2940, [\chi])\).

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

\( 48 q - 4 q^{4} + 14 q^{6} + 16 q^{9} + 4 q^{16} + 2 q^{21} - 6 q^{24} + 4 q^{25} - 2 q^{30} - 10 q^{36} + 6 q^{45} - 52 q^{46} - 4 q^{49} + 12 q^{61} + 8 q^{64} + 4 q^{70} - 16 q^{81} + 4 q^{84} - 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(2940, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2940.1.dd.a 2940.dd 2940.cd $24$ $1.467$ \(\Q(\zeta_{84})\) $D_{42}$ \(\Q(\sqrt{-5}) \) None 2940.1.dd.a \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{84}^{37}q^{2}-\zeta_{84}^{33}q^{3}-\zeta_{84}^{32}q^{4}+\cdots\)
2940.1.dd.b 2940.dd 2940.cd $24$ $1.467$ \(\Q(\zeta_{84})\) $D_{42}$ \(\Q(\sqrt{-5}) \) None 2940.1.dd.a \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{84}^{37}q^{2}+\zeta_{84}^{7}q^{3}-\zeta_{84}^{32}q^{4}+\cdots\)