Properties

Label 95.4.r
Level $95$
Weight $4$
Character orbit 95.r
Rep. character $\chi_{95}(2,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $336$
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.r (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
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 384 384 0
Cusp forms 336 336 0
Eisenstein series 48 48 0

Trace form

\( 336 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 12 q^{6} + 6 q^{7} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} - 264 q^{15} - 996 q^{16} + 132 q^{17} + 1116 q^{20} - 600 q^{21} + 468 q^{22} + 564 q^{23}+ \cdots + 1290 q^{98}+O(q^{100}) \) 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.r.a 95.r 95.r $336$ $5.605$ None 95.4.r.a \(-12\) \(-12\) \(-12\) \(6\) $\mathrm{SU}(2)[C_{36}]$