Properties

Label 2669.2.a
Level 2669
Weight 2
Character orbit a
Rep. character \(\chi_{2669}(1,\cdot)\)
Character field \(\Q\)
Dimension 209
Newforms 4
Sturm bound 474
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2669 = 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2669.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(474\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2669))\).

Total New Old
Modular forms 238 209 29
Cusp forms 235 209 26
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.

\(17\)\(157\)FrickeDim.
\(+\)\(+\)\(+\)\(44\)
\(+\)\(-\)\(-\)\(60\)
\(-\)\(+\)\(-\)\(60\)
\(-\)\(-\)\(+\)\(45\)
Plus space\(+\)\(89\)
Minus space\(-\)\(120\)

Trace form

\( 209q - q^{2} + 4q^{3} + 211q^{4} + 2q^{5} - 12q^{6} - 4q^{7} - 9q^{8} + 213q^{9} + O(q^{10}) \) \( 209q - q^{2} + 4q^{3} + 211q^{4} + 2q^{5} - 12q^{6} - 4q^{7} - 9q^{8} + 213q^{9} + 10q^{10} + 4q^{11} + 16q^{12} + 14q^{13} + 12q^{14} + 16q^{15} + 211q^{16} + q^{17} + 7q^{18} + 20q^{19} + 10q^{20} - 20q^{22} - 12q^{23} - 32q^{24} + 207q^{25} - 30q^{26} + 4q^{27} + 4q^{28} - 42q^{29} - 12q^{30} + 16q^{31} - 29q^{32} - 32q^{33} - q^{34} + 191q^{36} + 10q^{37} + 20q^{38} + 6q^{40} + 2q^{41} - 4q^{42} + 16q^{43} + 4q^{44} - 34q^{45} - 40q^{46} + 12q^{47} + 88q^{48} + 217q^{49} - 15q^{50} + 4q^{51} + 22q^{52} - 6q^{53} - 20q^{54} + 8q^{55} + 60q^{56} + 16q^{57} - 58q^{58} - 12q^{59} + 36q^{60} + 14q^{61} + 24q^{62} - 20q^{63} + 143q^{64} - 20q^{65} - 8q^{66} + 28q^{67} + 7q^{68} - 64q^{70} + 12q^{71} + 55q^{72} + 30q^{73} + 14q^{74} + 32q^{75} + 96q^{76} - 56q^{77} + 4q^{78} - 44q^{79} + 86q^{80} + 185q^{81} + 18q^{82} - 32q^{83} + 48q^{84} + 2q^{85} - 68q^{86} - 12q^{87} - 44q^{88} - 42q^{89} + 26q^{90} + 84q^{91} - 20q^{92} + 56q^{93} - 48q^{95} - 100q^{96} - 30q^{97} + 3q^{98} - 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2669))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17 157
2669.2.a.a \(44\) \(21.312\) None \(-3\) \(-8\) \(-6\) \(-6\) \(+\) \(+\)
2669.2.a.b \(45\) \(21.312\) None \(-2\) \(-20\) \(-10\) \(-20\) \(-\) \(-\)
2669.2.a.c \(60\) \(21.312\) None \(1\) \(24\) \(12\) \(12\) \(-\) \(+\)
2669.2.a.d \(60\) \(21.312\) None \(3\) \(8\) \(6\) \(10\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2669))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2669)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(157))\)\(^{\oplus 2}\)