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Properties

Label 8.5.d
Level $8$
Weight $5$
Character orbit 8.d
Rep. character $\chi_{8}(3,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $5$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 8.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(8, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3 q + 2 q^{2} - 2 q^{3} - 12 q^{4} - 68 q^{6} + 152 q^{8} + 25 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{2} - 2 q^{3} - 12 q^{4} - 68 q^{6} + 152 q^{8} + 25 q^{9} + 240 q^{10} - 98 q^{11} - 392 q^{12} - 480 q^{14} + 528 q^{16} - 122 q^{17} + 550 q^{18} + 702 q^{19} - 480 q^{20} - 132 q^{22} - 368 q^{24} - 45 q^{25} - 240 q^{26} - 1988 q^{27} + 960 q^{28} + 1440 q^{30} - 928 q^{32} + 332 q^{33} - 2748 q^{34} + 3840 q^{35} + 3100 q^{36} + 1468 q^{38} - 2880 q^{40} + 742 q^{41} - 2880 q^{42} - 7266 q^{43} - 8 q^{44} + 2400 q^{46} - 1952 q^{48} - 477 q^{49} + 3170 q^{50} + 10748 q^{51} + 480 q^{52} - 392 q^{54} + 5760 q^{56} - 4468 q^{57} + 2640 q^{58} - 10274 q^{59} - 2880 q^{60} - 9600 q^{62} + 3648 q^{64} + 1920 q^{65} + 2888 q^{66} + 10878 q^{67} - 15512 q^{68} - 3840 q^{70} + 3400 q^{72} + 10278 q^{73} + 13680 q^{74} - 12770 q^{75} + 3192 q^{76} - 1440 q^{78} + 13440 q^{80} - 4433 q^{81} - 6972 q^{82} + 6718 q^{83} + 5760 q^{84} - 10244 q^{86} - 5232 q^{88} - 14618 q^{89} - 10800 q^{90} - 3840 q^{91} - 4800 q^{92} + 16320 q^{94} - 26048 q^{96} + 7494 q^{97} + 12482 q^{98} - 2950 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.5.d.a 8.d 8.d $1$ $0.827$ \(\Q\) \(\Q(\sqrt{-2}) \) \(4\) \(-14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
8.5.d.b 8.d 8.d $2$ $0.827$ \(\Q(\sqrt{-15}) \) None \(-2\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)