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Properties

Label 312.2.bb
Level $312$
Weight $2$
Character orbit 312.bb
Rep. character $\chi_{312}(61,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 312.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(312, [\chi])\).

Total New Old
Modular forms 120 56 64
Cusp forms 104 56 48
Eisenstein series 16 0 16

Trace form

\( 56 q + 28 q^{9} + O(q^{10}) \) \( 56 q + 28 q^{9} + 4 q^{10} + 8 q^{12} - 16 q^{14} - 4 q^{16} - 4 q^{17} + 28 q^{20} - 8 q^{22} + 12 q^{24} - 64 q^{25} + 8 q^{26} + 16 q^{28} - 4 q^{30} + 40 q^{32} - 40 q^{34} - 48 q^{40} + 4 q^{41} + 4 q^{42} - 56 q^{44} - 16 q^{46} - 8 q^{48} - 36 q^{49} - 8 q^{50} + 12 q^{52} + 16 q^{55} - 12 q^{56} + 32 q^{57} - 20 q^{58} - 64 q^{60} + 16 q^{62} - 24 q^{64} - 28 q^{65} + 8 q^{66} - 32 q^{68} + 16 q^{70} - 64 q^{71} + 24 q^{73} - 24 q^{74} - 44 q^{76} - 8 q^{78} + 80 q^{79} + 20 q^{80} - 28 q^{81} - 4 q^{82} + 24 q^{87} + 20 q^{88} + 40 q^{89} + 8 q^{90} + 152 q^{92} + 8 q^{94} - 40 q^{95} - 40 q^{96} + 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(312, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
312.2.bb.a 312.bb 104.r $56$ $2.491$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)