Properties

Label 816.2.bx
Level $816$
Weight $2$
Character orbit 816.bx
Rep. character $\chi_{816}(325,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $288$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 816.bx (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
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 592 288 304
Cusp forms 560 288 272
Eisenstein series 32 0 32

Trace form

\( 288 q + O(q^{10}) \) \( 288 q - 32 q^{14} + 32 q^{19} + 24 q^{22} - 16 q^{24} + 32 q^{26} - 56 q^{28} + 80 q^{32} - 32 q^{34} - 8 q^{36} + 40 q^{40} + 24 q^{42} + 8 q^{44} + 8 q^{46} - 32 q^{48} - 8 q^{54} - 128 q^{55} + 24 q^{56} - 8 q^{60} - 32 q^{61} - 32 q^{65} + 40 q^{68} - 56 q^{70} - 24 q^{76} - 24 q^{78} + 88 q^{80} + 48 q^{82} + 64 q^{86} - 40 q^{88} - 8 q^{90} + 112 q^{91} - 96 q^{94} - 48 q^{96} + 32 q^{98} + O(q^{100}) \)

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.bx.a 816.bx 272.y $288$ $6.516$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(816, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(816, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 2}\)