Properties

Label 1776.1.bw
Level $1776$
Weight $1$
Character orbit 1776.bw
Rep. character $\chi_{1776}(1025,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $304$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1776.bw (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(304\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1776, [\chi])\).

Total New Old
Modular forms 36 6 30
Cusp forms 12 2 10
Eisenstein series 24 4 20

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + q^{3} - q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - q^{7} - q^{9} + q^{13} + 2q^{19} + q^{21} - q^{25} - 2q^{27} + 2q^{31} + 2q^{37} - q^{39} + 2q^{43} - 2q^{57} - 2q^{61} + 2q^{63} - q^{67} - 2q^{73} - 2q^{75} - q^{79} - q^{81} + q^{91} + q^{93} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1776, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1776.1.bw.a \(2\) \(0.886\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+\zeta_{6}q^{3}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1776, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1776, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 5}\)