Properties

Label 1601.2.a
Level $1601$
Weight $2$
Character orbit 1601.a
Rep. character $\chi_{1601}(1,\cdot)$
Character field $\Q$
Dimension $133$
Newform subspaces $2$
Sturm bound $267$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1601.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(267\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1601))\).

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.

\(1601\)Dim
\(+\)\(53\)
\(-\)\(80\)

Trace form

\( 133 q - q^{2} + 135 q^{4} - 4 q^{5} + 4 q^{7} - 3 q^{8} + 129 q^{9} + O(q^{10}) \) \( 133 q - q^{2} + 135 q^{4} - 4 q^{5} + 4 q^{7} - 3 q^{8} + 129 q^{9} - 10 q^{10} - 8 q^{12} - 2 q^{13} - 6 q^{14} + 12 q^{15} + 143 q^{16} - 4 q^{17} + 7 q^{18} - 2 q^{19} - 12 q^{20} + 4 q^{21} - 2 q^{22} + 6 q^{23} - 4 q^{24} + 125 q^{25} - 10 q^{26} + 24 q^{27} + 18 q^{28} - 4 q^{29} - 18 q^{30} + 22 q^{31} - 27 q^{32} + 24 q^{34} + 6 q^{35} + 109 q^{36} - 20 q^{38} + 20 q^{39} - 18 q^{40} - 26 q^{41} - 40 q^{42} - 12 q^{43} - 16 q^{44} - 34 q^{45} + 20 q^{46} - 16 q^{47} + 123 q^{49} - 29 q^{50} - 14 q^{51} + 12 q^{52} + 18 q^{53} - 52 q^{54} - 10 q^{55} - 40 q^{56} - 12 q^{57} + 38 q^{58} + 62 q^{60} - 2 q^{61} + 14 q^{63} + 185 q^{64} - 14 q^{65} - 58 q^{66} - 14 q^{67} - 4 q^{68} + 14 q^{69} - 22 q^{70} + 40 q^{71} - q^{72} + 2 q^{73} + 36 q^{74} + 6 q^{75} - 22 q^{76} - 14 q^{77} - 26 q^{78} + 30 q^{79} + 4 q^{80} + 117 q^{81} - 8 q^{82} - 18 q^{83} + 6 q^{84} - 50 q^{85} - 24 q^{86} - 18 q^{87} + 20 q^{88} - 28 q^{89} - 66 q^{90} + 12 q^{91} + 16 q^{92} + 34 q^{93} - 22 q^{95} - 88 q^{96} - 8 q^{97} - 39 q^{98} - 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1601))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 1601
1601.2.a.a 1601.a 1.a $53$ $12.784$ None \(-5\) \(-12\) \(-11\) \(-37\) $+$ $\mathrm{SU}(2)$
1601.2.a.b 1601.a 1.a $80$ $12.784$ None \(4\) \(12\) \(7\) \(41\) $-$ $\mathrm{SU}(2)$