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

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

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

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