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Properties

Label 2669.2.a
Level $2669$
Weight $2$
Character orbit 2669.a
Rep. character $\chi_{2669}(1,\cdot)$
Character field $\Q$
Dimension $209$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2669))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 17 157
2669.2.a.a 2669.a 1.a $44$ $21.312$ None \(-3\) \(-8\) \(-6\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$
2669.2.a.b 2669.a 1.a $45$ $21.312$ None \(-2\) \(-20\) \(-10\) \(-20\) $-$ $-$ $\mathrm{SU}(2)$
2669.2.a.c 2669.a 1.a $60$ $21.312$ None \(1\) \(24\) \(12\) \(12\) $-$ $+$ $\mathrm{SU}(2)$
2669.2.a.d 2669.a 1.a $60$ $21.312$ None \(3\) \(8\) \(6\) \(10\) $+$ $-$ $\mathrm{SU}(2)$

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

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