Properties

Label 552.2.f
Level $552$
Weight $2$
Character orbit 552.f
Rep. character $\chi_{552}(277,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $4$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
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 100 44 56
Cusp forms 92 44 48
Eisenstein series 8 0 8

Trace form

\( 44q - 12q^{8} - 44q^{9} + O(q^{10}) \) \( 44q - 12q^{8} - 44q^{9} - 4q^{10} - 8q^{12} - 4q^{14} + 24q^{16} + 8q^{17} - 4q^{20} - 20q^{22} + 12q^{24} - 52q^{25} + 16q^{26} - 8q^{30} - 24q^{31} - 20q^{32} + 8q^{34} + 4q^{38} + 16q^{39} + 36q^{40} - 8q^{41} + 12q^{42} - 24q^{44} + 48q^{47} + 60q^{49} + 16q^{50} - 12q^{56} - 16q^{57} + 24q^{58} - 24q^{60} + 48q^{62} - 32q^{65} - 16q^{66} + 44q^{68} + 16q^{70} - 64q^{71} + 12q^{72} + 24q^{73} - 64q^{74} + 60q^{76} - 16q^{78} - 28q^{80} + 44q^{81} + 24q^{84} + 12q^{86} + 24q^{87} - 68q^{88} + 40q^{89} + 4q^{90} - 8q^{94} - 48q^{95} - 20q^{96} + 8q^{97} - 56q^{98} + O(q^{100}) \)

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.f.a \(2\) \(4.408\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(8\) \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+2iq^{5}+\cdots\)
552.2.f.b \(4\) \(4.408\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) \(q+\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}+2q^{4}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
552.2.f.c \(18\) \(4.408\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{3}q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\beta _{9}q^{5}+\cdots\)
552.2.f.d \(20\) \(4.408\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+\beta _{11}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)