Properties

Label 529.2.a
Level $529$
Weight $2$
Character orbit 529.a
Rep. character $\chi_{529}(1,\cdot)$
Character field $\Q$
Dimension $31$
Newform subspaces $10$
Sturm bound $92$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 529 = 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 529.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(92\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(529))\).

Total New Old
Modular forms 58 52 6
Cusp forms 35 31 4
Eisenstein series 23 21 2

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

\(23\)Dim.
\(+\)\(13\)
\(-\)\(18\)

Trace form

\( 31q + q^{2} + 23q^{4} + 2q^{5} + 8q^{6} - 2q^{7} + 3q^{8} + 7q^{9} + O(q^{10}) \) \( 31q + q^{2} + 23q^{4} + 2q^{5} + 8q^{6} - 2q^{7} + 3q^{8} + 7q^{9} - 6q^{10} + 6q^{11} - 2q^{12} - 6q^{13} - 4q^{14} + 10q^{15} + 3q^{16} - 6q^{17} + 5q^{18} + 4q^{19} + 4q^{20} + 10q^{21} + 2q^{22} - 26q^{24} - 13q^{25} + 6q^{26} + 6q^{27} + 6q^{28} + 8q^{29} - 10q^{30} + 2q^{31} - 3q^{32} - 10q^{33} + 8q^{34} - 6q^{35} - 17q^{36} - 2q^{37} - 2q^{38} + 6q^{39} + 10q^{40} - 8q^{44} + 4q^{45} - 18q^{47} + 24q^{48} - 29q^{49} - 29q^{50} - 10q^{51} + 12q^{52} + 8q^{53} + 4q^{54} + 8q^{55} + 10q^{56} + 6q^{58} + 4q^{59} - 4q^{61} - 8q^{62} - 4q^{63} - 39q^{64} + 6q^{65} - 10q^{66} + 10q^{67} - 2q^{68} - 10q^{70} - 14q^{71} + 15q^{72} - 14q^{73} + 6q^{74} - 12q^{75} - 2q^{76} + 24q^{77} - 40q^{78} + 4q^{79} - 18q^{80} - 25q^{81} + 24q^{82} + 22q^{83} - 10q^{84} + 26q^{85} + 14q^{87} - 10q^{88} + 12q^{89} - 12q^{90} - 6q^{91} + 20q^{93} + 22q^{94} + 8q^{95} - 24q^{96} - 22q^{97} + 3q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(529))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
529.2.a.a \(2\) \(4.224\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(-2\) \(-\) \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
529.2.a.b \(2\) \(4.224\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-6\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots\)
529.2.a.c \(2\) \(4.224\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(6\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(3+\cdots)q^{6}+\cdots\)
529.2.a.d \(2\) \(4.224\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-4\) \(-\) \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
529.2.a.e \(2\) \(4.224\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(4\) \(-\) \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
529.2.a.f \(3\) \(4.224\) 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
529.2.a.g \(4\) \(4.224\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(0\) \(0\) \(+\) \(q-q^{2}+(-1+\beta _{2})q^{3}-q^{4}-\beta _{3}q^{5}+\cdots\)
529.2.a.h \(4\) \(4.224\) \(\Q(\sqrt{2}, \sqrt{13})\) None \(-2\) \(-4\) \(0\) \(0\) \(+\) \(q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{3})q^{4}+\cdots\)
529.2.a.i \(5\) \(4.224\) \(\Q(\zeta_{22})^+\) None \(2\) \(2\) \(-7\) \(-8\) \(+\) \(q+(\beta _{3}-\beta _{4})q^{2}+(1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots\)
529.2.a.j \(5\) \(4.224\) \(\Q(\zeta_{22})^+\) None \(2\) \(2\) \(7\) \(8\) \(-\) \(q+(\beta _{3}-\beta _{4})q^{2}+(1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(529))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(529)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)