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Properties

Label 3332.1.be
Level $3332$
Weight $1$
Character orbit 3332.be
Rep. character $\chi_{3332}(407,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $24$
Newform subspaces $3$
Sturm bound $504$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.be (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3332 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 3 \)
Sturm bound: \(504\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 24 24 0
Eisenstein series 24 24 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 24 q - 4 q^{4} - 4 q^{9} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 4 q^{21} - 4 q^{25} - 8 q^{26} - 8 q^{33} - 4 q^{36} - 4 q^{42} - 8 q^{53} - 4 q^{64} - 8 q^{66} + 24 q^{68} + 20 q^{69} - 8 q^{72} - 4 q^{77} + 16 q^{81} - 4 q^{84} - 8 q^{93} + 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3332.1.be.a 3332.be 3332.ae $6$ $1.663$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-17}) \) None 3332.1.be.a \(-1\) \(-5\) \(0\) \(1\) \(q+\zeta_{14}^{4}q^{2}+(-1+\zeta_{14}^{3})q^{3}-\zeta_{14}q^{4}+\cdots\)
3332.1.be.b 3332.be 3332.ae $6$ $1.663$ \(\Q(\zeta_{14})\) $D_{7}$ \(\Q(\sqrt{-17}) \) None 3332.1.be.a \(-1\) \(5\) \(0\) \(-1\) \(q+\zeta_{14}^{4}q^{2}+(1-\zeta_{14}^{3})q^{3}-\zeta_{14}q^{4}+\cdots\)
3332.1.be.c 3332.be 3332.ae $12$ $1.663$ \(\Q(\zeta_{28})\) $D_{14}$ \(\Q(\sqrt{-17}) \) None 3332.1.be.c \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{28}^{8}q^{2}+(\zeta_{28}^{7}+\zeta_{28}^{13})q^{3}-\zeta_{28}^{2}q^{4}+\cdots\)