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Properties

Label 1368.1.bz
Level $1368$
Weight $1$
Character orbit 1368.bz
Rep. character $\chi_{1368}(163,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $2$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1368.bz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + q^{2} - q^{4} - 2 q^{8} + O(q^{10}) \) \( 2 q + q^{2} - q^{4} - 2 q^{8} + 2 q^{11} - q^{16} + 2 q^{17} - q^{19} + q^{22} - q^{25} + q^{32} - 2 q^{34} - 2 q^{38} - q^{41} - 2 q^{43} - q^{44} + 2 q^{49} - 2 q^{50} - q^{59} + 2 q^{64} + q^{67} - 4 q^{68} + q^{73} - q^{76} + q^{82} + 2 q^{83} + 2 q^{86} - 2 q^{88} + 2 q^{89} + q^{97} + q^{98} + O(q^{100}) \)

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.bz.a 1368.bz 152.k $2$ $0.683$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+q^{11}-\zeta_{6}q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1368, [\chi]) \cong \)