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Properties

Label 1140.2.bt
Level $1140$
Weight $2$
Character orbit 1140.bt
Rep. character $\chi_{1140}(217,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $80$
Newform subspaces $1$
Sturm bound $480$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(480\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

Total New Old
Modular forms 1008 80 928
Cusp forms 912 80 832
Eisenstein series 96 0 96

Trace form

\( 80 q + 4 q^{5} + 8 q^{7} + O(q^{10}) \) \( 80 q + 4 q^{5} + 8 q^{7} + 16 q^{11} - 4 q^{17} - 24 q^{21} - 16 q^{23} - 12 q^{25} + 12 q^{33} + 4 q^{35} - 24 q^{41} + 32 q^{43} - 20 q^{47} - 36 q^{53} - 32 q^{55} - 8 q^{57} - 8 q^{61} + 4 q^{63} + 72 q^{67} - 24 q^{73} + 56 q^{77} + 40 q^{81} + 88 q^{83} + 32 q^{87} - 24 q^{91} + 16 q^{93} + 56 q^{95} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1140.2.bt.a 1140.bt 95.l $80$ $9.103$ None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)