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Properties

Label 336.3.bp
Level $336$
Weight $3$
Character orbit 336.bp
Rep. character $\chi_{336}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $256$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 528 256 272
Cusp forms 496 256 240
Eisenstein series 32 0 32

Trace form

\( 256 q - 12 q^{4} + 24 q^{8} + O(q^{10}) \) \( 256 q - 12 q^{4} + 24 q^{8} - 36 q^{10} - 32 q^{11} - 32 q^{14} - 4 q^{16} - 12 q^{18} - 160 q^{20} - 96 q^{22} + 128 q^{23} + 120 q^{28} + 64 q^{29} - 160 q^{34} - 96 q^{35} + 96 q^{37} - 280 q^{38} + 204 q^{40} + 60 q^{42} + 192 q^{43} + 124 q^{44} + 180 q^{46} + 288 q^{48} + 592 q^{50} - 24 q^{52} + 160 q^{53} - 56 q^{56} + 40 q^{58} - 128 q^{59} + 72 q^{60} - 1008 q^{62} - 192 q^{64} + 72 q^{66} + 256 q^{67} - 260 q^{68} - 132 q^{70} - 1024 q^{71} - 60 q^{72} - 528 q^{74} + 120 q^{76} + 72 q^{78} - 412 q^{80} + 1152 q^{81} - 260 q^{82} - 72 q^{84} + 212 q^{86} + 464 q^{88} + 480 q^{91} - 1688 q^{92} + 132 q^{94} - 300 q^{96} - 652 q^{98} + 192 q^{99} + O(q^{100}) \)

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.bp.a 336.bp 112.u $256$ $9.155$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{3}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)