Properties

Label 46.4.c
Level $46$
Weight $4$
Character orbit 46.c
Rep. character $\chi_{46}(3,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $60$
Newform subspaces $2$
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.c (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(46, [\chi])\).

Total New Old
Modular forms 200 60 140
Cusp forms 160 60 100
Eisenstein series 40 0 40

Trace form

\( 60 q + 8 q^{3} - 24 q^{4} + 10 q^{5} + 8 q^{6} - 8 q^{7} - 146 q^{9} + 20 q^{10} + 34 q^{11} + 32 q^{12} + 112 q^{13} - 40 q^{14} + 744 q^{15} - 96 q^{16} + 148 q^{17} + 40 q^{18} - 258 q^{19} - 312 q^{20}+ \cdots + 8964 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(46, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
46.4.c.a 46.c 23.c $30$ $2.714$ None 46.4.c.a \(-6\) \(6\) \(10\) \(107\) $\mathrm{SU}(2)[C_{11}]$
46.4.c.b 46.c 23.c $30$ $2.714$ None 46.4.c.b \(6\) \(2\) \(0\) \(-115\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(46, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)