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Properties

Label 336.3.x
Level $336$
Weight $3$
Character orbit 336.x
Rep. character $\chi_{336}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
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 264 96 168
Cusp forms 248 96 152
Eisenstein series 16 0 16

Trace form

\( 96 q - 12 q^{4} + O(q^{10}) \) \( 96 q - 12 q^{4} + 40 q^{10} - 32 q^{11} + 48 q^{12} + 28 q^{14} - 60 q^{16} - 12 q^{18} + 64 q^{19} - 76 q^{22} + 128 q^{23} - 72 q^{24} + 200 q^{26} - 32 q^{29} - 144 q^{30} - 320 q^{32} - 32 q^{34} - 24 q^{36} + 96 q^{37} - 56 q^{38} - 360 q^{40} - 224 q^{43} + 228 q^{44} + 88 q^{46} + 672 q^{49} + 300 q^{50} + 192 q^{51} + 48 q^{52} + 160 q^{53} + 72 q^{54} + 512 q^{55} + 196 q^{56} - 52 q^{58} + 72 q^{60} + 64 q^{61} + 48 q^{62} + 252 q^{64} + 64 q^{65} - 32 q^{67} + 376 q^{68} - 192 q^{69} - 168 q^{70} - 60 q^{72} - 828 q^{74} - 384 q^{75} - 264 q^{76} - 224 q^{77} - 216 q^{78} - 80 q^{80} - 864 q^{81} - 440 q^{82} + 320 q^{83} - 320 q^{85} - 452 q^{86} - 236 q^{88} + 48 q^{90} - 432 q^{92} - 1368 q^{94} + 360 q^{96} - 96 q^{99} + O(q^{100}) \)

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.x.a 336.x 16.f $96$ $9.155$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)