Properties

Label 312.2.ba
Level $312$
Weight $2$
Character orbit 312.ba
Rep. character $\chi_{312}(179,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 312.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 312 \)
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 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9} + O(q^{10}) \) \( 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9} + 6 q^{10} + 8 q^{12} - 6 q^{16} - 12 q^{19} + 8 q^{22} - 36 q^{24} - 88 q^{25} + 16 q^{27} + 12 q^{28} + 14 q^{30} - 6 q^{33} + 22 q^{36} + 4 q^{40} + 26 q^{42} - 20 q^{43} - 36 q^{46} + 14 q^{48} - 24 q^{49} - 20 q^{51} - 16 q^{52} - 36 q^{54} - 66 q^{58} + 28 q^{64} + 32 q^{66} - 12 q^{67} - 66 q^{72} + 2 q^{75} - 60 q^{76} - 14 q^{78} - 2 q^{81} + 50 q^{82} - 90 q^{84} + 24 q^{88} + 8 q^{90} + 44 q^{91} + 72 q^{94} + 12 q^{97} + O(q^{100}) \)

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.ba.a 312.ba 312.aa $104$ $2.491$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$