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Properties

Label 816.2.cf
Level $816$
Weight $2$
Character orbit 816.cf
Rep. character $\chi_{816}(29,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1120$
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.cf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 816 \)
Character field: \(\Q(\zeta_{16})\)
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 1184 1184 0
Cusp forms 1120 1120 0
Eisenstein series 64 64 0

Trace form

\( 1120 q - 8 q^{3} - 16 q^{4} - 8 q^{6} + O(q^{10}) \) \( 1120 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{10} - 32 q^{12} - 16 q^{15} - 16 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{24} - 8 q^{27} - 64 q^{28} - 8 q^{30} - 32 q^{31} - 16 q^{34} - 8 q^{36} - 16 q^{37} + 48 q^{39} + 48 q^{40} - 24 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 32 q^{49} + 72 q^{51} - 32 q^{52} - 8 q^{54} + 48 q^{58} - 8 q^{60} + 48 q^{61} - 16 q^{63} - 16 q^{64} - 24 q^{66} - 16 q^{69} - 80 q^{70} + 96 q^{72} - 8 q^{75} - 80 q^{76} + 40 q^{78} - 32 q^{79} - 16 q^{81} + 80 q^{82} + 64 q^{84} - 16 q^{85} - 16 q^{88} - 280 q^{90} + 96 q^{91} - 8 q^{93} + 96 q^{94} - 112 q^{96} - 32 q^{97} - 8 q^{99} + O(q^{100}) \)

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.cf.a 816.cf 816.bf $1120$ $6.516$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$