Properties

Label 276.2.k
Level $276$
Weight $2$
Character orbit 276.k
Rep. character $\chi_{276}(5,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $80$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.k (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
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 540 80 460
Cusp forms 420 80 340
Eisenstein series 120 0 120

Trace form

\( 80q - 2q^{3} + 6q^{9} + O(q^{10}) \) \( 80q - 2q^{3} + 6q^{9} - 4q^{13} + 11q^{15} + 33q^{21} + 25q^{27} + 20q^{31} + 11q^{33} - 44q^{37} - 18q^{39} - 44q^{43} - 100q^{49} - 98q^{55} - 33q^{57} - 44q^{61} - 55q^{63} - 22q^{67} - 41q^{69} - 26q^{73} - 65q^{75} - 44q^{79} - 42q^{81} + 2q^{85} - 64q^{87} - 46q^{93} + 66q^{97} - 66q^{99} + O(q^{100}) \)

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.k.a \(80\) \(2.204\) None \(0\) \(-2\) \(0\) \(0\)

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

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