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Properties

Label 2040.1.cj
Level $2040$
Weight $1$
Character orbit 2040.cj
Rep. character $\chi_{2040}(149,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $4$
Sturm bound $432$
Trace bound $18$

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Defining parameters

Level: \( N \) \(=\) \( 2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2040.cj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2040 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(432\)
Trace bound: \(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2040, [\chi])\).

Total New Old
Modular forms 32 32 0
Cusp forms 16 16 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 16 0 0 0

Trace form

\( 16 q - 8 q^{4} - 4 q^{6} + O(q^{10}) \) \( 16 q - 8 q^{4} - 4 q^{6} - 4 q^{10} + 4 q^{24} - 8 q^{30} + 16 q^{31} + 4 q^{34} + 8 q^{39} + 4 q^{40} - 8 q^{46} + 4 q^{54} - 8 q^{64} - 16 q^{79} - 16 q^{81} + 4 q^{90} + 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2040, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2040.1.cj.a 2040.cj 2040.bj $4$ $1.018$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-30}) \) None 2040.1.cj.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots\)
2040.1.cj.b 2040.cj 2040.bj $4$ $1.018$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-30}) \) None 2040.1.cj.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}+\zeta_{8}^{3}q^{6}+\cdots\)
2040.1.cj.c 2040.cj 2040.bj $4$ $1.018$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-15}) \) None 2040.1.cj.c \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
2040.1.cj.d 2040.cj 2040.bj $4$ $1.018$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-15}) \) None 2040.1.cj.c \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots\)