↑

Properties

Label 1607.2.a
Level $1607$
Weight $2$
Character orbit 1607.a
Rep. character $\chi_{1607}(1,\cdot)$
Character field $\Q$
Dimension $134$
Newform subspaces $3$
Sturm bound $268$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1607 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1607.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 \(M_{2}(\Gamma_0(1607))\).

Total New Old
Modular forms 135 135 0
Cusp forms 134 134 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.

\(1607\)Dim
\(+\)\(54\)
\(-\)\(80\)

Trace form

\( 134 q - q^{2} + 131 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 3 q^{8} + 136 q^{9} + O(q^{10}) \) \( 134 q - q^{2} + 131 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 3 q^{8} + 136 q^{9} - 2 q^{10} - 6 q^{11} - 10 q^{12} + 8 q^{13} - 10 q^{14} - 6 q^{15} + 121 q^{16} + 8 q^{17} - 15 q^{18} + 2 q^{19} - 8 q^{20} - 2 q^{21} - 16 q^{22} - 12 q^{23} - 20 q^{24} + 142 q^{25} + 22 q^{26} + 8 q^{28} - 6 q^{29} - 40 q^{30} - 2 q^{31} + 5 q^{32} + 6 q^{33} - 10 q^{35} + 133 q^{36} - 6 q^{39} - 2 q^{40} - 4 q^{41} - 6 q^{42} - 2 q^{43} - 6 q^{44} - 26 q^{45} - 34 q^{46} - 10 q^{47} - 20 q^{48} + 128 q^{49} - 5 q^{50} + 2 q^{51} + 34 q^{52} - 6 q^{53} + 4 q^{54} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 12 q^{58} + 24 q^{59} + 2 q^{60} + 2 q^{61} + 58 q^{62} - 8 q^{63} + 105 q^{64} - 16 q^{65} + 48 q^{66} - 2 q^{67} + 12 q^{68} - 4 q^{69} + 20 q^{70} + 24 q^{71} - 3 q^{72} + 46 q^{73} - 8 q^{74} - 34 q^{75} + 12 q^{76} - 18 q^{77} + 8 q^{78} + 18 q^{79} - 26 q^{80} + 126 q^{81} + 72 q^{82} + 6 q^{83} - 34 q^{84} - 12 q^{85} - 14 q^{86} - 26 q^{87} - 52 q^{88} - 12 q^{89} - 22 q^{90} + 18 q^{91} + 4 q^{92} - 8 q^{93} - 60 q^{94} + 2 q^{95} - 14 q^{96} + 36 q^{97} + 17 q^{98} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1607))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 1607
1607.2.a.a 1607.a 1.a $1$ $12.832$ \(\Q\) None \(-1\) \(1\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
1607.2.a.b 1607.a 1.a $53$ $12.832$ None \(-9\) \(-13\) \(-14\) \(-27\) $+$ $\mathrm{SU}(2)$
1607.2.a.c 1607.a 1.a $80$ $12.832$ None \(9\) \(12\) \(10\) \(31\) $-$ $\mathrm{SU}(2)$