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Properties

Label 95.5.d
Level $95$
Weight $5$
Character orbit 95.d
Rep. character $\chi_{95}(94,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $5$
Sturm bound $50$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(50\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(95, [\chi])\).

Total New Old
Modular forms 42 42 0
Cusp forms 38 38 0
Eisenstein series 4 4 0

Trace form

\( 38 q + 256 q^{4} - 11 q^{5} - 104 q^{6} + 914 q^{9} + O(q^{10}) \) \( 38 q + 256 q^{4} - 11 q^{5} - 104 q^{6} + 914 q^{9} + 110 q^{11} + 2008 q^{16} - 266 q^{19} - 2148 q^{20} + 416 q^{24} - 347 q^{25} + 3280 q^{26} - 816 q^{30} + 75 q^{35} + 320 q^{36} + 4024 q^{39} - 6912 q^{44} + 2547 q^{45} - 15012 q^{49} - 3696 q^{54} + 8993 q^{55} - 5786 q^{61} + 2568 q^{64} - 27960 q^{66} + 48064 q^{74} - 30840 q^{76} - 45112 q^{80} - 22698 q^{81} + 28785 q^{85} + 35233 q^{95} + 79712 q^{96} + 25666 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.5.d.a 95.d 95.d $2$ $9.820$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(31\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{4}q^{4}+(14+3\beta )q^{5}+(5-10\beta )q^{7}+\cdots\)
95.5.d.b 95.d 95.d $2$ $9.820$ \(\Q(\sqrt{19}) \) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(50\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-4\beta q^{3}+3q^{4}+5^{2}q^{5}-76q^{6}+\cdots\)
95.5.d.c 95.d 95.d $2$ $9.820$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(50\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3\beta q^{2}-2\beta q^{3}+29q^{4}+5^{2}q^{5}+\cdots\)
95.5.d.d 95.d 95.d $4$ $9.820$ \(\Q(\sqrt{10}, \sqrt{38})\) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(-100\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(4\beta _{1}-3\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
95.5.d.e 95.d 95.d $28$ $9.820$ None \(0\) \(0\) \(-42\) \(0\) $\mathrm{SU}(2)[C_{2}]$