Properties

Label 618.2.a
Level 618
Weight 2
Character orbit a
Rep. character \(\chi_{618}(1,\cdot)\)
Character field \(\Q\)
Dimension 17
Newforms 11
Sturm bound 208
Trace bound 5

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Defining parameters

Level: \( N \) = \( 618 = 2 \cdot 3 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 618.a (trivial)
Character field: \(\Q\)
Newforms: \( 11 \)
Sturm bound: \(208\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(618))\).

Total New Old
Modular forms 108 17 91
Cusp forms 101 17 84
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(103\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(11\)

Trace form

\(17q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 17q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(17q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 17q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut q^{24} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 24q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 9q^{49} \) \(\mathstrut +\mathstrut 31q^{50} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut q^{54} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 17q^{64} \) \(\mathstrut +\mathstrut 20q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut -\mathstrut 54q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 16q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 17q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 28q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut +\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut -\mathstrut 28q^{93} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 32q^{95} \) \(\mathstrut -\mathstrut q^{96} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut 9q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(618))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 103
618.2.a.a \(1\) \(4.935\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
618.2.a.b \(1\) \(4.935\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
618.2.a.c \(1\) \(4.935\) \(\Q\) None \(-1\) \(1\) \(-3\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+2q^{7}+\cdots\)
618.2.a.d \(1\) \(4.935\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
618.2.a.e \(1\) \(4.935\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
618.2.a.f \(1\) \(4.935\) \(\Q\) None \(1\) \(1\) \(-4\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-4q^{7}+\cdots\)
618.2.a.g \(1\) \(4.935\) \(\Q\) None \(1\) \(1\) \(3\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-2q^{7}+\cdots\)
618.2.a.h \(2\) \(4.935\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(6\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
618.2.a.i \(2\) \(4.935\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
618.2.a.j \(2\) \(4.935\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+(2+\beta )q^{7}+\cdots\)
618.2.a.k \(4\) \(4.935\) 4.4.54332.1 None \(4\) \(-4\) \(5\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(618))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(618)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(103))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(206))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(309))\)\(^{\oplus 2}\)