Properties

Label 671.2.a
Level 671
Weight 2
Character orbit 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 about

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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 61
671.2.a.a \(5\) \(5.358\) 5.5.24217.1 None \(-2\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
671.2.a.b \(6\) \(5.358\) 6.6.2661761.1 None \(0\) \(-1\) \(-1\) \(-5\) \(+\) \(+\) \(q+\beta _{3}q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
671.2.a.c \(19\) \(5.358\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(5\) \(0\) \(0\) \(9\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
671.2.a.d \(21\) \(5.358\) None \(0\) \(3\) \(7\) \(5\) \(+\) \(-\)

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

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