Properties

Label 276.2.i
Level $276$
Weight $2$
Character orbit 276.i
Rep. character $\chi_{276}(13,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $40$
Newform subspaces $2$
Sturm bound $96$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 540 40 500
Cusp forms 420 40 380
Eisenstein series 120 0 120

Trace form

\( 40q - 4q^{5} - 4q^{7} - 4q^{9} + O(q^{10}) \) \( 40q - 4q^{5} - 4q^{7} - 4q^{9} - 8q^{13} - 4q^{15} + 10q^{17} + 26q^{19} + 4q^{21} + 44q^{23} + 32q^{25} + 6q^{29} + 30q^{31} - 28q^{35} - 28q^{37} - 36q^{39} - 36q^{41} - 32q^{43} - 4q^{45} - 72q^{47} - 4q^{49} - 40q^{51} - 48q^{53} - 6q^{55} - 32q^{57} - 28q^{59} + 44q^{61} - 4q^{63} + 16q^{65} + 50q^{67} - 4q^{69} + 14q^{73} + 8q^{75} + 16q^{77} - 20q^{79} - 4q^{81} - 28q^{83} - 22q^{85} - 8q^{87} - 56q^{89} - 88q^{91} + 8q^{93} - 82q^{95} - 28q^{97} + 22q^{99} + O(q^{100}) \)

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.i.a \(20\) \(2.204\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-2\) \(-4\) \(0\) \(q+\beta _{17}q^{3}+(\beta _{3}+\beta _{4}-\beta _{9}-\beta _{10}+\beta _{15}+\cdots)q^{5}+\cdots\)
276.2.i.b \(20\) \(2.204\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(2\) \(0\) \(-4\) \(q-\beta _{5}q^{3}+(1-\beta _{3}+\beta _{5}+\beta _{7}+\beta _{10}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(276, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)