Properties

Label 123.2.a
Level $123$
Weight $2$
Character orbit 123.a
Rep. character $\chi_{123}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(123))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 41
123.2.a.a 123.a 1.a $1$ $0.982$ \(\Q\) None \(-2\) \(1\) \(-4\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots\)
123.2.a.b 123.a 1.a $1$ $0.982$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-2q^{5}-4q^{7}+q^{9}+5q^{11}+\cdots\)
123.2.a.c 123.a 1.a $2$ $0.982$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2-\beta )q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
123.2.a.d 123.a 1.a $3$ $0.982$ 3.3.316.1 None \(1\) \(-3\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

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