Properties

Label 183.2.a
Level 183
Weight 2
Character orbit a
Rep. character \(\chi_{183}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 3
Sturm bound 41
Trace bound 1

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Defining parameters

Level: \( N \) = \( 183 = 3 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 183.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(41\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(183))\).

Total New Old
Modular forms 22 11 11
Cusp forms 19 11 8
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.

\(3\)\(61\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(6\)
Plus space\(+\)\(2\)
Minus space\(-\)\(9\)

Trace form

\(11q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 11q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(11q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 11q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 16q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 13q^{16} \) \(\mathstrut +\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 13q^{36} \) \(\mathstrut -\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 20q^{42} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 48q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 10q^{51} \) \(\mathstrut +\mathstrut 26q^{52} \) \(\mathstrut +\mathstrut 6q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 5q^{64} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 38q^{68} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 18q^{73} \) \(\mathstrut +\mathstrut 42q^{74} \) \(\mathstrut +\mathstrut 31q^{75} \) \(\mathstrut -\mathstrut 60q^{76} \) \(\mathstrut +\mathstrut 44q^{77} \) \(\mathstrut -\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 18q^{80} \) \(\mathstrut +\mathstrut 11q^{81} \) \(\mathstrut +\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 28q^{83} \) \(\mathstrut +\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 28q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut +\mathstrut 32q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut -\mathstrut 56q^{95} \) \(\mathstrut -\mathstrut 15q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 51q^{98} \) \(\mathstrut -\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(183))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 61
183.2.a.a \(2\) \(1.461\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
183.2.a.b \(3\) \(1.461\) 3.3.148.1 None \(1\) \(-3\) \(6\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+2q^{5}+\cdots\)
183.2.a.c \(6\) \(1.461\) 6.6.91407488.1 None \(0\) \(6\) \(2\) \(2\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(183))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(183)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 2}\)