↑

Properties

Label 663.2.cr
Level $663$
Weight $2$
Character orbit 663.cr
Rep. character $\chi_{663}(29,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $1280$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 663.cr (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 663 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(663, [\chi])\).

Total New Old
Modular forms 1408 1408 0
Cusp forms 1280 1280 0
Eisenstein series 128 128 0

Trace form

\( 1280 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} + O(q^{10}) \) \( 1280 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 32 q^{12} - 32 q^{13} - 8 q^{15} - 128 q^{18} - 16 q^{19} - 32 q^{21} - 16 q^{22} - 8 q^{24} - 128 q^{25} - 32 q^{27} + 32 q^{28} - 8 q^{30} - 128 q^{31} - 64 q^{34} + 8 q^{36} - 16 q^{37} - 64 q^{40} + 40 q^{42} - 16 q^{43} + 56 q^{45} - 48 q^{46} - 56 q^{48} + 16 q^{49} - 32 q^{51} - 8 q^{54} + 16 q^{55} - 192 q^{57} + 48 q^{58} - 112 q^{60} - 16 q^{61} - 8 q^{63} - 192 q^{64} - 208 q^{66} + 80 q^{69} - 128 q^{70} + 64 q^{72} - 64 q^{73} - 8 q^{75} - 16 q^{76} - 120 q^{78} - 64 q^{79} - 8 q^{81} + 112 q^{82} - 112 q^{85} - 56 q^{87} + 112 q^{88} + 128 q^{90} - 64 q^{91} - 72 q^{93} + 48 q^{94} - 128 q^{96} - 16 q^{97} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(663, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
663.2.cr.a 663.cr 663.br $1280$ $5.294$ None \(0\) \(-8\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{48}]$