Properties

Label 2352.1.by
Level $2352$
Weight $1$
Character orbit 2352.by
Rep. character $\chi_{2352}(335,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $12$
Newform subspaces $2$
Sturm bound $448$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2352.by (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 2 \)
Sturm bound: \(448\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2352, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 12 12 0
Eisenstein series 72 0 72

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q - 2q^{9} + O(q^{10}) \) \( 12q - 2q^{9} + 2q^{21} + 2q^{25} - 10q^{37} - 2q^{49} + 4q^{57} - 14q^{61} - 2q^{81} - 4q^{93} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2352.1.by.a \(6\) \(1.174\) \(\Q(\zeta_{14})\) \(D_{14}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-\zeta_{14}q^{3}+\zeta_{14}^{5}q^{7}+\zeta_{14}^{2}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots\)
2352.1.by.b \(6\) \(1.174\) \(\Q(\zeta_{14})\) \(D_{14}\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+\zeta_{14}q^{3}-\zeta_{14}^{5}q^{7}+\zeta_{14}^{2}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots\)