Properties

Label 46.4.a
Level $46$
Weight $4$
Character orbit 46.a
Rep. character $\chi_{46}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 46.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(46))\).

Total New Old
Modular forms 20 6 14
Cusp forms 16 6 10
Eisenstein series 4 0 4

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
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(2\)

Trace form

\( 6 q - 8 q^{3} + 24 q^{4} - 10 q^{5} - 8 q^{6} + 8 q^{7} + 146 q^{9} - 20 q^{10} - 34 q^{11} - 32 q^{12} - 112 q^{13} + 40 q^{14} + 4 q^{15} + 96 q^{16} + 28 q^{17} - 128 q^{18} + 38 q^{19} - 40 q^{20} - 260 q^{21}+ \cdots + 2586 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(46))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 23
46.4.a.a 46.a 1.a $1$ $2.714$ \(\Q\) None 46.4.a.a \(-2\) \(-1\) \(-10\) \(-12\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+4q^{4}-10q^{5}+2q^{6}+\cdots\)
46.4.a.b 46.a 1.a $1$ $2.714$ \(\Q\) None 46.4.a.b \(2\) \(-9\) \(-20\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-9q^{3}+4q^{4}-20q^{5}-18q^{6}+\cdots\)
46.4.a.c 46.a 1.a $2$ $2.714$ \(\Q(\sqrt{41}) \) None 46.4.a.c \(-4\) \(-1\) \(10\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)
46.4.a.d 46.a 1.a $2$ $2.714$ \(\Q(\sqrt{73}) \) None 46.4.a.d \(4\) \(3\) \(10\) \(12\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(46))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(46)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)