Properties

Label 57.2.a
Level 57
Weight 2
Character orbit a
Rep. character \(\chi_{57}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 13
Trace bound 3

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Defining parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 57.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(13\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(57))\).

Total New Old
Modular forms 8 3 5
Cusp forms 5 3 2
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.

\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3q - 3q^{2} + q^{3} + 3q^{4} - 4q^{5} + q^{6} - 2q^{7} - 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - 3q^{2} + q^{3} + 3q^{4} - 4q^{5} + q^{6} - 2q^{7} - 3q^{8} + 3q^{9} + 2q^{10} - 2q^{11} - q^{12} + 2q^{13} + 4q^{14} + 2q^{15} - 9q^{16} - 4q^{17} - 3q^{18} - 3q^{19} - 2q^{20} + 8q^{21} + 4q^{22} + 4q^{23} - 3q^{24} - q^{25} + 14q^{26} + q^{27} - 4q^{28} - 10q^{29} - 10q^{30} + 4q^{31} + 21q^{32} - 4q^{33} - 10q^{34} + 18q^{35} + 3q^{36} - 2q^{37} + 3q^{38} - 2q^{39} + 6q^{40} - 10q^{41} - 16q^{42} - 6q^{43} - 4q^{44} - 4q^{45} + 4q^{46} + 6q^{47} - q^{48} + 13q^{49} - q^{50} - 2q^{51} - 14q^{52} - 2q^{53} + q^{54} - 6q^{55} - q^{57} + 26q^{58} - 20q^{59} + 10q^{60} + 4q^{61} + 16q^{62} - 2q^{63} - 9q^{64} - 24q^{65} + 8q^{66} + 12q^{67} + 10q^{68} + 12q^{69} - 36q^{70} - 3q^{72} - 12q^{73} - 26q^{74} - 9q^{75} - 3q^{76} - 14q^{77} + 22q^{78} + 16q^{79} + 10q^{80} + 3q^{81} + 14q^{82} + 32q^{83} + 16q^{84} + 18q^{85} - 6q^{87} + 2q^{89} + 2q^{90} - 28q^{91} - 4q^{92} + 16q^{93} + 24q^{94} + 4q^{95} + 5q^{96} - 2q^{97} - 47q^{98} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(57))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 19
57.2.a.a \(1\) \(0.455\) \(\Q\) None \(-2\) \(-1\) \(-3\) \(-5\) \(+\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
57.2.a.b \(1\) \(0.455\) \(\Q\) None \(-2\) \(1\) \(1\) \(3\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
57.2.a.c \(1\) \(0.455\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(57))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(57)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)