Properties

Label 3920.1.fc
Level $3920$
Weight $1$
Character orbit 3920.fc
Rep. character $\chi_{3920}(319,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $24$
Newform subspaces $1$
Sturm bound $672$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3920.fc (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 980 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(672\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3920, [\chi])\).

Total New Old
Modular forms 240 24 216
Cusp forms 96 24 72
Eisenstein series 144 0 144

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

\( 24q - 2q^{5} + 18q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 18q^{9} + 6q^{21} + 2q^{25} - 10q^{29} - 4q^{41} - 4q^{45} - 2q^{49} + 2q^{61} - 12q^{69} - 12q^{81} - 2q^{89} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3920.1.fc.a \(24\) \(1.956\) \(\Q(\zeta_{84})\) \(D_{42}\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{84}^{15}+\zeta_{84}^{35})q^{3}-\zeta_{84}^{32}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)