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Properties

Label 50.4.e
Level $50$
Weight $4$
Character orbit 50.e
Rep. character $\chi_{50}(9,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $32$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 50.e (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(50, [\chi])\).

Total New Old
Modular forms 96 32 64
Cusp forms 80 32 48
Eisenstein series 16 0 16

Trace form

\( 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9} - 40 q^{10} - 106 q^{11} + 80 q^{12} + 56 q^{14} + 260 q^{15} - 128 q^{16} + 320 q^{17} + 110 q^{19} - 160 q^{20} - 36 q^{21} - 360 q^{22} - 370 q^{23} - 192 q^{24}+ \cdots - 2108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(50, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
50.4.e.a 50.e 25.e $32$ $2.950$ None 50.4.e.a \(0\) \(0\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{4}^{\mathrm{old}}(50, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(50, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)