Properties

Label 552.2.n
Level $552$
Weight $2$
Character orbit 552.n
Rep. character $\chi_{552}(91,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $2$
Sturm bound $192$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.n (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 184 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(552, [\chi])\).

Total New Old
Modular forms 100 48 52
Cusp forms 92 48 44
Eisenstein series 8 0 8

Trace form

\( 48q - 4q^{2} + 8q^{4} - 4q^{6} - 4q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - 4q^{2} + 8q^{4} - 4q^{6} - 4q^{8} + 48q^{9} + 8q^{16} - 4q^{18} - 4q^{24} + 48q^{25} - 4q^{32} + 8q^{36} - 40q^{46} + 48q^{49} - 84q^{50} - 4q^{54} - 80q^{62} + 8q^{64} - 4q^{72} + 48q^{81} - 80q^{82} - 12q^{92} - 8q^{94} - 4q^{96} - 20q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(552, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
552.2.n.a \(24\) \(4.408\) None \(-4\) \(24\) \(0\) \(0\)
552.2.n.b \(24\) \(4.408\) None \(0\) \(-24\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(552, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)