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Properties

Label 1609.2.a
Level $1609$
Weight $2$
Character orbit 1609.a
Rep. character $\chi_{1609}(1,\cdot)$
Character field $\Q$
Dimension $133$
Newform subspaces $3$
Sturm bound $268$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1609 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1609.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(268\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1609))\).

Total New Old
Modular forms 134 134 0
Cusp forms 133 133 0
Eisenstein series 1 1 0

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

\(1609\)Dim
\(+\)\(60\)
\(-\)\(73\)

Trace form

\( 133 q - q^{2} - 4 q^{3} + 129 q^{4} - 4 q^{5} - 6 q^{6} - 4 q^{7} - 3 q^{8} + 125 q^{9} + O(q^{10}) \) \( 133 q - q^{2} - 4 q^{3} + 129 q^{4} - 4 q^{5} - 6 q^{6} - 4 q^{7} - 3 q^{8} + 125 q^{9} - 18 q^{10} - 12 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} + 117 q^{16} - 10 q^{17} + 17 q^{18} - 12 q^{19} - 10 q^{20} - 10 q^{21} + 6 q^{22} + 14 q^{23} + 4 q^{24} + 121 q^{25} - 2 q^{26} - 22 q^{27} - 6 q^{28} - 4 q^{29} + 2 q^{30} - 26 q^{31} - 7 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{35} + 91 q^{36} - 20 q^{37} - 6 q^{38} + 6 q^{39} - 44 q^{40} - 24 q^{41} - 8 q^{42} + 20 q^{44} - 46 q^{45} + 12 q^{46} - 2 q^{47} - 18 q^{48} + 95 q^{49} - 27 q^{50} - 10 q^{51} + 20 q^{52} + 10 q^{54} - 20 q^{55} - 10 q^{56} - 22 q^{57} + 28 q^{58} + 4 q^{60} - 40 q^{61} + 66 q^{62} - 18 q^{63} + 139 q^{64} - 18 q^{65} - 14 q^{66} - 10 q^{67} - 40 q^{68} - 34 q^{69} + 28 q^{70} - 6 q^{71} + 41 q^{72} - 12 q^{73} + 50 q^{74} - 42 q^{75} - 30 q^{76} + 26 q^{77} + 14 q^{78} + 4 q^{79} - 12 q^{80} + 93 q^{81} - 20 q^{82} + 36 q^{83} - 20 q^{84} + 20 q^{85} - 10 q^{86} + 56 q^{87} + 30 q^{88} - 10 q^{89} - 126 q^{90} - 34 q^{91} + 68 q^{92} + 28 q^{93} - 36 q^{94} + 34 q^{95} - 48 q^{97} + 19 q^{98} + 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1609))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 1609
1609.2.a.a 1609.a 1.a $2$ $12.848$ \(\Q(\sqrt{5}) \) None \(-3\) \(3\) \(-6\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots\)
1609.2.a.b 1609.a 1.a $58$ $12.848$ None \(-10\) \(-15\) \(-9\) \(-23\) $+$ $\mathrm{SU}(2)$
1609.2.a.c 1609.a 1.a $73$ $12.848$ None \(12\) \(8\) \(11\) \(15\) $-$ $\mathrm{SU}(2)$