Properties

Label 756.1.bk
Level $756$
Weight $1$
Character orbit 756.bk
Rep. character $\chi_{756}(53,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 756.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(756, [\chi])\).

Total New Old
Modular forms 50 2 48
Cusp forms 14 2 12
Eisenstein series 36 0 36

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

\( 2q - q^{7} + O(q^{10}) \) \( 2q - q^{7} + 4q^{13} + q^{19} - q^{25} + q^{31} - 2q^{37} - 2q^{43} - q^{49} + q^{61} - 2q^{67} + q^{73} - 2q^{79} - 2q^{91} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
756.1.bk.a \(2\) \(0.377\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{7}+q^{13}-\zeta_{6}^{2}q^{19}-\zeta_{6}q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 3}\)