Properties

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

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Defining parameters

Level: \( N \) = \( 671 = 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 671.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(671))\) into irreducible Hecke orbits

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

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