Properties

Label 276.2.g
Level $276$
Weight $2$
Character orbit 276.g
Rep. character $\chi_{276}(137,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(276, [\chi])\).

Total New Old
Modular forms 54 8 46
Cusp forms 42 8 34
Eisenstein series 12 0 12

Trace form

\( 8q + 2q^{3} - 6q^{9} + O(q^{10}) \) \( 8q + 2q^{3} - 6q^{9} + 4q^{13} + 8q^{27} - 20q^{31} + 18q^{39} - 32q^{49} + 32q^{55} - 14q^{69} + 4q^{73} - 34q^{75} - 46q^{81} - 24q^{85} - 2q^{87} + 46q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(276, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
276.2.g.a \(8\) \(2.204\) 8.0.\(\cdots\).7 None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(276, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(276, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)