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Properties

Label 1368.1.bt
Level $1368$
Weight $1$
Character orbit 1368.bt
Rep. character $\chi_{1368}(635,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1368.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1368 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(240\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1368, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 4 q^{4} + 2 q^{6} - 2 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{4} + 2 q^{6} - 2 q^{9} + 3 q^{11} + 4 q^{16} - 6 q^{17} - q^{19} - 3 q^{22} + 2 q^{24} + 2 q^{25} - 2 q^{36} - 3 q^{38} - 3 q^{41} + 4 q^{43} + 3 q^{44} - 2 q^{49} + 3 q^{51} - 4 q^{54} + 3 q^{59} + 4 q^{64} - 6 q^{68} + q^{73} + 3 q^{75} - q^{76} - 2 q^{81} + q^{82} - 3 q^{88} + 2 q^{96} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1368.1.bt.a 1368.bt 1368.at $2$ $0.683$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(-2\) \(-1\) \(0\) \(0\) \(q-q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}-q^{8}+\cdots\)
1368.1.bt.b 1368.bt 1368.at $2$ $0.683$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-2}) \) None \(2\) \(1\) \(0\) \(0\) \(q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}+q^{8}+\cdots\)