↑

Properties

Label 671.2.a
Level $671$
Weight $2$
Character orbit 671.a
Rep. character $\chi_{671}(1,\cdot)$
Character field $\Q$
Dimension $51$
Newform subspaces $4$
Sturm bound $124$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(124\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(671))\).

Total New Old
Modular forms 64 51 13
Cusp forms 61 51 10
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.

\(11\)\(61\)FrickeDim
\(+\)\(+\)$+$\(6\)
\(+\)\(-\)$-$\(21\)
\(-\)\(+\)$-$\(19\)
\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(11\)
Minus space\(-\)\(40\)

Trace form

\( 51 q + 3 q^{2} + 2 q^{3} + 57 q^{4} + 4 q^{5} + 8 q^{7} - 9 q^{8} + 61 q^{9} + O(q^{10}) \) \( 51 q + 3 q^{2} + 2 q^{3} + 57 q^{4} + 4 q^{5} + 8 q^{7} - 9 q^{8} + 61 q^{9} + 6 q^{10} - 3 q^{11} + 8 q^{12} + 14 q^{13} + 4 q^{14} + 2 q^{15} + 73 q^{16} + 2 q^{17} - q^{18} + 16 q^{19} - 14 q^{20} + 20 q^{21} + 3 q^{22} - 2 q^{23} + 8 q^{24} + 67 q^{25} + 10 q^{26} - 34 q^{27} + 12 q^{28} + 10 q^{29} - 12 q^{30} + 6 q^{31} + 15 q^{32} - 2 q^{33} + 6 q^{34} - 28 q^{35} + 101 q^{36} + 16 q^{37} - 20 q^{38} - 8 q^{39} - 6 q^{40} + 10 q^{41} - 20 q^{42} + 36 q^{43} - 11 q^{44} + 22 q^{45} + 24 q^{46} - 12 q^{47} - 64 q^{48} + 91 q^{49} + 29 q^{50} + 32 q^{51} + 22 q^{52} + 6 q^{53} - 16 q^{54} - 8 q^{55} + 24 q^{56} + 44 q^{57} - 14 q^{58} - 34 q^{59} - 28 q^{60} + q^{61} + 4 q^{63} + 113 q^{64} + 48 q^{65} - 8 q^{66} + 22 q^{67} - 18 q^{68} - 34 q^{69} - 28 q^{70} - 18 q^{71} - 37 q^{72} + 22 q^{73} - 26 q^{74} - 52 q^{75} + 4 q^{76} + 8 q^{77} - 112 q^{78} + 48 q^{79} - 50 q^{80} + 123 q^{81} - 42 q^{82} - 4 q^{83} - 60 q^{84} + 56 q^{85} - 32 q^{86} - 36 q^{87} + 15 q^{88} - 126 q^{90} + 48 q^{91} + 12 q^{92} - 42 q^{93} + 12 q^{94} - 36 q^{95} - 44 q^{96} + 60 q^{97} - 77 q^{98} - 9 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(671))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 61
671.2.a.a 671.a 1.a $5$ $5.358$ 5.5.24217.1 None \(-2\) \(0\) \(-2\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
671.2.a.b 671.a 1.a $6$ $5.358$ 6.6.2661761.1 None \(0\) \(-1\) \(-1\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
671.2.a.c 671.a 1.a $19$ $5.358$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(5\) \(0\) \(0\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
671.2.a.d 671.a 1.a $21$ $5.358$ None \(0\) \(3\) \(7\) \(5\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(671))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(671)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 2}\)