Properties

Label 2736.2.cg
Level $2736$
Weight $2$
Character orbit 2736.cg
Rep. character $\chi_{2736}(1151,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $3$
Sturm bound $960$
Trace bound $19$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.cg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(960\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 1008 80 928
Cusp forms 912 80 832
Eisenstein series 96 0 96

Trace form

\( 80q + O(q^{10}) \) \( 80q + 8q^{13} + 40q^{25} + 16q^{37} - 64q^{49} - 8q^{61} + 8q^{73} + 48q^{85} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2736.2.cg.a \(24\) \(21.847\) None \(0\) \(0\) \(0\) \(0\)
2736.2.cg.b \(24\) \(21.847\) None \(0\) \(0\) \(0\) \(0\)
2736.2.cg.c \(32\) \(21.847\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)