Properties

Label 95.4.l
Level $95$
Weight $4$
Character orbit 95.l
Rep. character $\chi_{95}(8,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 95.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(95, [\chi])\).

Total New Old
Modular forms 128 128 0
Cusp forms 112 112 0
Eisenstein series 16 16 0

Trace form

\( 112 q - 6 q^{2} - 6 q^{3} + 6 q^{5} - 16 q^{6} - 16 q^{7} - 6 q^{10} - 72 q^{11} - 6 q^{13} + 246 q^{15} + 736 q^{16} + 14 q^{17} - 1024 q^{20} - 300 q^{21} - 486 q^{22} - 138 q^{23} + 182 q^{25} + 48 q^{26}+ \cdots + 10500 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.4.l.a 95.l 95.l $112$ $5.605$ None 95.4.l.a \(-6\) \(-6\) \(6\) \(-16\) $\mathrm{SU}(2)[C_{12}]$