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Properties

Label 816.2.bs
Level $816$
Weight $2$
Character orbit 816.bs
Rep. character $\chi_{816}(155,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $560$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 816.bs (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 816 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(816, [\chi])\).

Total New Old
Modular forms 592 592 0
Cusp forms 560 560 0
Eisenstein series 32 32 0

Trace form

\( 560 q - 4 q^{3} - 12 q^{6} - 16 q^{7} + O(q^{10}) \) \( 560 q - 4 q^{3} - 12 q^{6} - 16 q^{7} - 24 q^{10} - 24 q^{12} - 16 q^{16} - 8 q^{18} - 16 q^{22} - 12 q^{24} - 4 q^{27} + 16 q^{28} - 32 q^{31} - 16 q^{33} - 8 q^{34} - 20 q^{36} - 8 q^{37} - 8 q^{39} - 56 q^{40} - 32 q^{42} + 16 q^{45} + 48 q^{46} + 48 q^{48} - 16 q^{49} - 44 q^{51} - 16 q^{52} - 48 q^{54} + 24 q^{57} + 8 q^{58} - 72 q^{60} - 40 q^{61} + 80 q^{63} - 108 q^{66} - 16 q^{67} - 8 q^{69} - 56 q^{70} + 40 q^{72} - 36 q^{75} + 56 q^{76} - 48 q^{78} - 8 q^{82} - 8 q^{84} - 8 q^{85} - 8 q^{87} - 120 q^{88} + 64 q^{90} + 96 q^{91} - 32 q^{94} - 16 q^{96} - 16 q^{97} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(816, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
816.2.bs.a 816.bs 816.as $560$ $6.516$ None \(0\) \(-4\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{8}]$