Properties

Label 473.2.a
Level 473
Weight 2
Character orbit a
Rep. character \(\chi_{473}(1,\cdot)\)
Character field \(\Q\)
Dimension 35
Newforms 7
Sturm bound 88
Trace bound 3

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Defining parameters

Level: \( N \) = \( 473 = 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 473.a (trivial)
Character field: \(\Q\)
Newforms: \( 7 \)
Sturm bound: \(88\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(473))\).

Total New Old
Modular forms 46 35 11
Cusp forms 43 35 8
Eisenstein series 3 0 3

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

\(11\)\(43\)FrickeDim.
\(+\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(15\)
Minus space\(-\)\(20\)

Trace form

\( 35q + q^{2} + 2q^{3} + 31q^{4} - 4q^{5} - 8q^{6} + 8q^{7} - 15q^{8} + 41q^{9} + O(q^{10}) \) \( 35q + q^{2} + 2q^{3} + 31q^{4} - 4q^{5} - 8q^{6} + 8q^{7} - 15q^{8} + 41q^{9} - 14q^{10} - 3q^{11} - 12q^{12} - 2q^{13} - 16q^{14} - 22q^{15} + 35q^{16} - 14q^{17} - 19q^{18} + 2q^{20} + 20q^{21} + 3q^{22} - 10q^{23} - 8q^{24} + 31q^{25} - 2q^{26} - 10q^{27} - 8q^{28} + 10q^{29} + 24q^{30} - 2q^{31} - 39q^{32} + 2q^{33} - 38q^{34} + 12q^{35} + 39q^{36} - 4q^{37} - 4q^{38} - 8q^{39} - 50q^{40} + 18q^{41} + 32q^{42} + q^{43} - 3q^{44} - 2q^{45} + 12q^{46} - 36q^{47} - 24q^{48} + 79q^{49} + 35q^{50} + 18q^{52} - 22q^{53} - 16q^{54} - 8q^{56} - 20q^{57} - 34q^{58} - 6q^{59} - 4q^{60} - 10q^{61} + 52q^{62} - 68q^{63} - 5q^{64} - 56q^{65} - 16q^{66} - 6q^{67} - 14q^{68} - 26q^{69} + 12q^{70} + 18q^{71} - 43q^{72} + 22q^{73} + 54q^{74} + 12q^{75} - 8q^{76} + 4q^{77} - 12q^{78} + 40q^{79} + 10q^{80} + 59q^{81} - 58q^{82} - 8q^{83} + 48q^{84} - 36q^{85} - 7q^{86} - 8q^{87} - 9q^{88} - 8q^{89} + 2q^{90} + 56q^{91} + 16q^{92} + 14q^{93} - 8q^{94} - 16q^{95} + 56q^{96} - 8q^{97} - 7q^{98} - 9q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(473))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 43
473.2.a.a \(1\) \(3.777\) \(\Q\) None \(-2\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{9}+\cdots\)
473.2.a.b \(2\) \(3.777\) \(\Q(\sqrt{5}) \) None \(1\) \(-4\) \(2\) \(0\) \(+\) \(+\) \(q+\beta q^{2}-2q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
473.2.a.c \(2\) \(3.777\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(2\) \(-4\) \(-\) \(-\) \(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+2\beta q^{5}+\cdots\)
473.2.a.d \(5\) \(3.777\) 5.5.173513.1 None \(-3\) \(-1\) \(-4\) \(-9\) \(-\) \(-\) \(q+(-1-\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+\cdots\)
473.2.a.e \(5\) \(3.777\) 5.5.38569.1 None \(1\) \(-3\) \(-6\) \(-15\) \(+\) \(+\) \(q+(\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+\cdots\)
473.2.a.f \(9\) \(3.777\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(4\) \(5\) \(0\) \(19\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
473.2.a.g \(11\) \(3.777\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-1\) \(6\) \(3\) \(17\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{8})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(473))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(473)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 2}\)