Properties

Label 123.2.d
Level 123
Weight 2
Character orbit d
Rep. character \(\chi_{123}(40,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 28
Trace bound 0

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Defining parameters

Level: \( N \) = \( 123 = 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 123.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(123, [\chi])\).

Total New Old
Modular forms 16 8 8
Cusp forms 12 8 4
Eisenstein series 4 0 4

Trace form

\( 8q + 2q^{2} + 10q^{4} - 8q^{5} - 6q^{8} - 8q^{9} + O(q^{10}) \) \( 8q + 2q^{2} + 10q^{4} - 8q^{5} - 6q^{8} - 8q^{9} - 4q^{10} + 6q^{16} - 2q^{18} - 8q^{20} - 4q^{21} - 4q^{23} + 8q^{25} + 26q^{31} - 10q^{32} - 10q^{33} - 10q^{36} + 10q^{37} - 8q^{39} - 36q^{40} + 30q^{41} + 20q^{42} - 2q^{43} + 8q^{45} - 8q^{46} - 8q^{49} + 34q^{50} - 6q^{51} + 12q^{57} - 24q^{59} + 6q^{61} - 40q^{62} - 42q^{64} + 6q^{72} - 18q^{73} + 100q^{74} + 36q^{77} + 28q^{78} - 44q^{80} + 8q^{81} - 18q^{82} + 36q^{84} - 28q^{86} - 26q^{87} + 4q^{90} + 16q^{91} + 84q^{92} - 38q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(123, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
123.2.d.a \(8\) \(0.982\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(2\) \(0\) \(-8\) \(0\) \(q+\beta _{4}q^{2}+\beta _{3}q^{3}+(1-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(123, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(123, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)