↑

Properties

Label 336.3.br
Level $336$
Weight $3$
Character orbit 336.br
Rep. character $\chi_{336}(59,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $496$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(336, [\chi])\).

Total New Old
Modular forms 528 528 0
Cusp forms 496 496 0
Eisenstein series 32 32 0

Trace form

\( 496 q - 6 q^{3} - 4 q^{4} - 16 q^{7} + O(q^{10}) \) \( 496 q - 6 q^{3} - 4 q^{4} - 16 q^{7} - 12 q^{10} - 6 q^{12} - 20 q^{16} + 64 q^{18} - 12 q^{19} - 22 q^{21} + 8 q^{22} - 6 q^{24} + 116 q^{28} - 30 q^{30} - 12 q^{33} - 272 q^{36} - 4 q^{37} - 4 q^{39} + 48 q^{40} - 70 q^{42} - 16 q^{43} - 6 q^{45} - 36 q^{46} - 16 q^{49} - 46 q^{51} + 384 q^{52} + 78 q^{54} + 380 q^{58} - 330 q^{60} - 12 q^{61} + 32 q^{64} - 666 q^{66} - 132 q^{67} - 108 q^{70} - 158 q^{72} - 156 q^{75} + 52 q^{78} - 4 q^{81} - 744 q^{82} - 176 q^{84} + 184 q^{85} - 12 q^{87} + 268 q^{88} + 480 q^{91} + 34 q^{93} - 624 q^{94} + 96 q^{96} + 316 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.3.br.a 336.br 336.ar $496$ $9.155$ None \(0\) \(-6\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{12}]$