Properties

Label 95.9.d
Level $95$
Weight $9$
Character orbit 95.d
Rep. character $\chi_{95}(94,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $6$
Sturm bound $90$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 95.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(90\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(95, [\chi])\).

Total New Old
Modular forms 82 82 0
Cusp forms 78 78 0
Eisenstein series 4 4 0

Trace form

\( 78 q + 9248 q^{4} - 281 q^{5} + 1240 q^{6} + 161834 q^{9} + O(q^{10}) \) \( 78 q + 9248 q^{4} - 281 q^{5} + 1240 q^{6} + 161834 q^{9} + 18794 q^{11} + 950616 q^{16} - 138530 q^{19} - 1037028 q^{20} - 1242592 q^{24} + 268663 q^{25} - 706352 q^{26} - 5353776 q^{30} + 2336445 q^{35} + 17239328 q^{36} - 7907144 q^{39} + 5067648 q^{44} + 8454897 q^{45} - 60649432 q^{49} + 53893584 q^{54} - 361057 q^{55} + 44577042 q^{61} + 2861960 q^{64} + 179012616 q^{66} - 142678784 q^{74} - 205983384 q^{76} - 307086712 q^{80} + 395201934 q^{81} - 88996185 q^{85} + 60991963 q^{95} - 759712 q^{96} + 402988294 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.9.d.a 95.d 95.d $1$ $38.701$ \(\Q\) \(\Q(\sqrt{-95}) \) \(-13\) \(142\) \(625\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-13q^{2}+142q^{3}-87q^{4}+5^{4}q^{5}+\cdots\)
95.9.d.b 95.d 95.d $1$ $38.701$ \(\Q\) \(\Q(\sqrt{-95}) \) \(13\) \(-142\) \(625\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+13q^{2}-142q^{3}-87q^{4}+5^{4}q^{5}+\cdots\)
95.9.d.c 95.d 95.d $2$ $38.701$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-289\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{8}q^{4}+(-191+93\beta )q^{5}+(-365+\cdots)q^{7}+\cdots\)
95.9.d.d 95.d 95.d $2$ $38.701$ \(\Q(\sqrt{95}) \) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(1250\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3\beta q^{2}-8\beta q^{3}+599q^{4}+5^{4}q^{5}+\cdots\)
95.9.d.e 95.d 95.d $4$ $38.701$ \(\Q(\sqrt{2}, \sqrt{95})\) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(-2500\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+2\beta _{2})q^{2}+(-5\beta _{1}+13\beta _{2})q^{3}+\cdots\)
95.9.d.f 95.d 95.d $68$ $38.701$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$