Properties

Label 552.2.m
Level $552$
Weight $2$
Character orbit 552.m
Rep. character $\chi_{552}(137,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

Trace form

\( 24q + 4q^{9} + O(q^{10}) \) \( 24q + 4q^{9} + 16q^{25} - 12q^{27} + 8q^{31} - 20q^{39} + 8q^{49} + 32q^{55} - 16q^{69} + 8q^{75} + 12q^{81} - 24q^{85} - 28q^{87} - 12q^{93} + O(q^{100}) \)

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.m.a \(8\) \(4.408\) 8.0.40960000.1 None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{3}+\beta _{3}q^{5}+\beta _{5}q^{7}+(1+\cdots)q^{9}+\cdots\)
552.2.m.b \(16\) \(4.408\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{7}q^{3}-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)