Properties

Label 3920.1.bt
Level $3920$
Weight $1$
Character orbit 3920.bt
Rep. character $\chi_{3920}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $6$
Sturm bound $672$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3920.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(672\)
Trace bound: \(11\)

Dimensions

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

Total New Old
Modular forms 184 20 164
Cusp forms 88 20 68
Eisenstein series 96 0 96

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20q - 2q^{5} - 8q^{9} + O(q^{10}) \) \( 20q - 2q^{5} - 8q^{9} + 2q^{25} + 4q^{29} - 4q^{41} - 4q^{45} + 2q^{61} - 12q^{69} - 10q^{81} - 2q^{89} + O(q^{100}) \)

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.bt.a \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{25}+q^{29}+\cdots\)
3920.1.bt.b \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{25}+q^{29}+\cdots\)
3920.1.bt.c \(4\) \(1.956\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{4}q^{5}+(-1+\cdots)q^{9}+\cdots\)
3920.1.bt.d \(4\) \(1.956\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-1+\cdots)q^{9}+\cdots\)
3920.1.bt.e \(4\) \(1.956\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{5}+(-1+\cdots)q^{9}+\cdots\)
3920.1.bt.f \(4\) \(1.956\) \(\Q(\zeta_{12})\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{35}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{3}q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)