Properties

Label 123.2.a
Level 123
Weight 2
Character orbit a
Rep. character \(\chi_{123}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 4
Sturm bound 28
Trace bound 2

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Defining parameters

Level: \( N \) = \( 123 = 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 123.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(28\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(123))\).

Total New Old
Modular forms 16 7 9
Cusp forms 13 7 6
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.

\(3\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(5\)

Trace form

\( 7q - q^{2} - q^{3} + 3q^{4} + 2q^{5} - 3q^{6} - 8q^{7} + 3q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - q^{2} - q^{3} + 3q^{4} + 2q^{5} - 3q^{6} - 8q^{7} + 3q^{8} + 7q^{9} + 10q^{10} + q^{12} + 2q^{13} - 4q^{14} - 2q^{15} - 9q^{16} + 2q^{17} - q^{18} - 8q^{19} - 10q^{20} - 4q^{21} - 8q^{22} - 12q^{23} - 3q^{24} + 17q^{25} - 2q^{26} - q^{27} - 12q^{28} + 2q^{29} - 2q^{30} - 6q^{31} + 15q^{32} - 2q^{33} - 2q^{34} + 12q^{35} + 3q^{36} + 4q^{37} - 6q^{39} + 2q^{40} + q^{41} + 20q^{42} + 6q^{43} - 24q^{44} + 2q^{45} + 8q^{46} + 32q^{47} - 15q^{48} + 15q^{49} - 35q^{50} + 8q^{51} + 14q^{52} + 2q^{53} - 3q^{54} - 24q^{56} - 8q^{57} - 18q^{58} - 20q^{59} - 6q^{60} - 12q^{61} + 24q^{62} - 8q^{63} - 17q^{64} + 48q^{65} + 12q^{66} + 12q^{67} + 42q^{68} + 4q^{70} - 32q^{71} + 3q^{72} + 8q^{73} + 58q^{74} + 9q^{75} + 16q^{76} - 12q^{77} + 2q^{78} - 16q^{79} + 10q^{80} + 7q^{81} - q^{82} - 44q^{83} + 4q^{84} - 24q^{85} + 8q^{86} + 12q^{87} + 10q^{89} + 10q^{90} + 8q^{91} - 20q^{92} + 8q^{93} + 8q^{94} - 28q^{95} + q^{96} - 14q^{97} + 11q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(123))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 41
123.2.a.a \(1\) \(0.982\) \(\Q\) None \(-2\) \(1\) \(-4\) \(-2\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots\)
123.2.a.b \(1\) \(0.982\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) \(+\) \(+\) \(q-q^{3}-2q^{4}-2q^{5}-4q^{7}+q^{9}+5q^{11}+\cdots\)
123.2.a.c \(2\) \(0.982\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(-4\) \(-\) \(+\) \(q+\beta q^{2}+q^{3}+(2-\beta )q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
123.2.a.d \(3\) \(0.982\) 3.3.316.1 None \(1\) \(-3\) \(4\) \(2\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(123))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(123)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 2}\)