Properties

Label 552.2.a
Level $552$
Weight $2$
Character orbit 552.a
Rep. character $\chi_{552}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $7$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(552))\).

Total New Old
Modular forms 104 10 94
Cusp forms 89 10 79
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(7\)

Trace form

\( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 4q^{13} - 4q^{15} - 4q^{17} + 4q^{19} + 4q^{21} + 22q^{25} + 2q^{27} - 12q^{29} + 12q^{33} + 8q^{37} + 4q^{39} - 4q^{41} + 4q^{43} + 4q^{45} - 8q^{47} + 10q^{49} + 12q^{53} - 16q^{55} + 4q^{57} - 8q^{59} + 24q^{61} - 8q^{65} - 4q^{67} - 4q^{69} - 24q^{71} + 4q^{73} + 14q^{75} + 10q^{81} - 24q^{83} - 24q^{85} - 12q^{87} - 36q^{89} + 16q^{91} - 56q^{95} + 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(552))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 23
552.2.a.a \(1\) \(4.408\) \(\Q\) None \(0\) \(-1\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
552.2.a.b \(1\) \(4.408\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
552.2.a.c \(1\) \(4.408\) \(\Q\) None \(0\) \(-1\) \(2\) \(-4\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
552.2.a.d \(1\) \(4.408\) \(\Q\) None \(0\) \(-1\) \(4\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
552.2.a.e \(1\) \(4.408\) \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots\)
552.2.a.f \(2\) \(4.408\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
552.2.a.g \(3\) \(4.408\) 3.3.148.1 None \(0\) \(3\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+\beta _{2}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(552)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 2}\)