Properties

Label 95.4.g
Level $95$
Weight $4$
Character orbit 95.g
Rep. character $\chi_{95}(18,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 95.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 64 64 0
Cusp forms 56 56 0
Eisenstein series 8 8 0

Trace form

\( 56 q - 12 q^{5} - 32 q^{6} - 8 q^{7} + 48 q^{11} - 640 q^{16} - 164 q^{17} - 128 q^{20} - 444 q^{23} + 28 q^{25} + 24 q^{26} + 792 q^{28} - 600 q^{30} + 1176 q^{35} + 2872 q^{36} - 488 q^{38} - 2160 q^{42}+ \cdots + 5720 q^{96}+O(q^{100}) \) 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.g.a 95.g 95.g $4$ $5.605$ \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) 95.4.g.a \(0\) \(0\) \(-28\) \(-72\) $\mathrm{U}(1)[D_{4}]$ \(q-8\beta _{1}q^{4}+(-7+2\beta _{3})q^{5}+(-18+\cdots)q^{7}+\cdots\)
95.4.g.b 95.g 95.g $52$ $5.605$ None 95.4.g.b \(0\) \(0\) \(16\) \(64\) $\mathrm{SU}(2)[C_{4}]$