Properties

Label 663.2.m
Level $663$
Weight $2$
Character orbit 663.m
Rep. character $\chi_{663}(200,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 663 = 3 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 663.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 663 \)
Character field: \(\Q(i)\)
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 176 176 0
Cusp forms 160 160 0
Eisenstein series 16 16 0

Trace form

\( 160 q - 4 q^{3} - 8 q^{7} + O(q^{10}) \) \( 160 q - 4 q^{3} - 8 q^{7} + 16 q^{10} - 8 q^{12} - 12 q^{13} + 12 q^{15} - 152 q^{16} - 20 q^{18} + 4 q^{19} - 12 q^{21} - 8 q^{22} + 8 q^{24} - 128 q^{25} + 8 q^{27} + 8 q^{31} + 4 q^{33} + 16 q^{34} - 48 q^{39} + 24 q^{40} - 8 q^{43} + 112 q^{49} - 8 q^{51} + 24 q^{52} + 40 q^{54} - 64 q^{55} + 32 q^{60} - 48 q^{61} - 8 q^{67} + 16 q^{70} - 40 q^{72} + 36 q^{75} + 16 q^{76} + 60 q^{78} + 32 q^{79} - 24 q^{81} + 48 q^{82} + 36 q^{84} + 76 q^{85} + 48 q^{88} + 24 q^{90} - 20 q^{91} + 12 q^{93} - 80 q^{97} + O(q^{100}) \)

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.m.a 663.m 663.m $160$ $5.294$ None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$