Properties

Label 163.2.a
Level 163
Weight 2
Character orbit a
Rep. character \(\chi_{163}(1,\cdot)\)
Character field \(\Q\)
Dimension 13
Newforms 3
Sturm bound 27
Trace bound 1

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Defining parameters

Level: \( N \) = \( 163 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 163.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(27\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(163))\).

Total New Old
Modular forms 14 14 0
Cusp forms 13 13 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.

\(163\)Dim.
\(+\)\(6\)
\(-\)\(7\)

Trace form

\(13q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 14q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 10q^{20} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 10q^{31} \) \(\mathstrut -\mathstrut 26q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 18q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 10q^{39} \) \(\mathstrut +\mathstrut 24q^{40} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 40q^{42} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 9q^{47} \) \(\mathstrut -\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 14q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut -\mathstrut 3q^{61} \) \(\mathstrut +\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 18q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 38q^{70} \) \(\mathstrut +\mathstrut 23q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 10q^{75} \) \(\mathstrut -\mathstrut 26q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut -\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut +\mathstrut 11q^{83} \) \(\mathstrut -\mathstrut 64q^{84} \) \(\mathstrut +\mathstrut 40q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 50q^{87} \) \(\mathstrut -\mathstrut 22q^{88} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut +\mathstrut 42q^{92} \) \(\mathstrut -\mathstrut 30q^{93} \) \(\mathstrut +\mathstrut 56q^{94} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 84q^{96} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut 14q^{98} \) \(\mathstrut +\mathstrut 18q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(163))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 163
163.2.a.a \(1\) \(1.302\) \(\Q\) None \(0\) \(0\) \(-4\) \(2\) \(+\) \(q-2q^{4}-4q^{5}+2q^{7}-3q^{9}-6q^{11}+\cdots\)
163.2.a.b \(5\) \(1.302\) 5.5.65657.1 None \(-5\) \(-5\) \(-9\) \(-6\) \(+\) \(q+(-1+\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
163.2.a.c \(7\) \(1.302\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(1\) \(11\) \(0\) \(-\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(2-\beta _{6})q^{5}+\cdots\)