Properties

Label 46.2.a
Level 46
Weight 2
Character orbit a
Rep. character \(\chi_{46}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 46 = 2 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 46.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(46))\).

Total New Old
Modular forms 8 1 7
Cusp forms 5 1 4
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.

\(2\)\(23\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q - q^{2} + q^{4} + 4q^{5} - 4q^{7} - q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} + 4q^{5} - 4q^{7} - q^{8} - 3q^{9} - 4q^{10} + 2q^{11} - 2q^{13} + 4q^{14} + q^{16} - 2q^{17} + 3q^{18} - 2q^{19} + 4q^{20} - 2q^{22} + q^{23} + 11q^{25} + 2q^{26} - 4q^{28} + 2q^{29} - q^{32} + 2q^{34} - 16q^{35} - 3q^{36} - 4q^{37} + 2q^{38} - 4q^{40} + 6q^{41} + 10q^{43} + 2q^{44} - 12q^{45} - q^{46} + 9q^{49} - 11q^{50} - 2q^{52} - 4q^{53} + 8q^{55} + 4q^{56} - 2q^{58} + 12q^{59} - 8q^{61} + 12q^{63} + q^{64} - 8q^{65} - 10q^{67} - 2q^{68} + 16q^{70} + 3q^{72} + 6q^{73} + 4q^{74} - 2q^{76} - 8q^{77} - 12q^{79} + 4q^{80} + 9q^{81} - 6q^{82} + 14q^{83} - 8q^{85} - 10q^{86} - 2q^{88} - 6q^{89} + 12q^{90} + 8q^{91} + q^{92} - 8q^{95} + 6q^{97} - 9q^{98} - 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(46))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 23
46.2.a.a \(1\) \(0.367\) \(\Q\) None \(-1\) \(0\) \(4\) \(-4\) \(+\) \(-\) \(q-q^{2}+q^{4}+4q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(46))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(46)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)