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Properties

Label 336.3.bv
Level $336$
Weight $3$
Character orbit 336.bv
Rep. character $\chi_{336}(61,\cdot)$
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.bv (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

\( 256 q - 12 q^{4} - 24 q^{8} + O(q^{10}) \) \( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50} + 720 q^{52} + 160 q^{53} - 56 q^{56} - 312 q^{58} + 384 q^{59} + 72 q^{60} - 96 q^{64} - 216 q^{66} - 320 q^{67} - 780 q^{68} - 828 q^{70} + 60 q^{72} - 88 q^{74} - 72 q^{78} - 612 q^{80} + 1152 q^{81} + 780 q^{82} - 72 q^{84} - 212 q^{86} - 464 q^{88} - 480 q^{91} - 488 q^{92} - 612 q^{94} + 768 q^{95} - 900 q^{96} - 196 q^{98} + 192 q^{99} + O(q^{100}) \)

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

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

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