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Properties

Label 3844.1.i
Level $3844$
Weight $1$
Character orbit 3844.i
Rep. character $\chi_{3844}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $22$
Newform subspaces $6$
Sturm bound $496$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3844 = 2^{2} \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3844.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 124 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(496\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3844, [\chi])\).

Total New Old
Modular forms 94 78 16
Cusp forms 30 22 8
Eisenstein series 64 56 8

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 18 4 0 0

Trace form

\( 22 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} - 9 q^{9} + O(q^{10}) \) \( 22 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} - 9 q^{9} + 3 q^{10} - 2 q^{13} + 5 q^{14} + 16 q^{16} + 2 q^{17} + 2 q^{18} + 5 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{24} - 5 q^{25} - 3 q^{28} - 4 q^{30} - 4 q^{32} - 4 q^{33} - 6 q^{36} + 2 q^{37} + q^{38} + 2 q^{41} - 3 q^{49} + 3 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{54} - 2 q^{56} - 2 q^{57} + 14 q^{64} - 2 q^{65} - 2 q^{68} - 10 q^{70} - q^{72} + 2 q^{73} - 3 q^{76} - 4 q^{77} - 4 q^{78} + q^{80} - 7 q^{81} + q^{82} - 2 q^{84} - 4 q^{85} + 2 q^{86} - 2 q^{88} + 3 q^{90} + 2 q^{96} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3844, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3844.1.i.a 3844.i 124.i $2$ $1.918$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(-1\) \(-3\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
3844.1.i.b 3844.i 124.i $2$ $1.918$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(-1\) \(3\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+(1-\zeta_{6}^{2}+\cdots)q^{7}+\cdots\)
3844.1.i.c 3844.i 124.i $2$ $1.918$ \(\Q(\sqrt{-3}) \) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-31}) \) \(\Q(\sqrt{31}) \) \(2\) \(0\) \(2\) \(0\) \(q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
3844.1.i.d 3844.i 124.i $4$ $1.918$ \(\Q(\zeta_{12})\) $A_{4}$ None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
3844.1.i.e 3844.i 124.i $4$ $1.918$ \(\Q(\sqrt{2}, \sqrt{-3})\) $D_{4}$ \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+(-1-\beta _{2})q^{9}-\beta _{1}q^{13}+\cdots\)
3844.1.i.f 3844.i 124.i $8$ $1.918$ 8.0.339738624.2 $D_{8}$ \(\Q(\sqrt{-1}) \) None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+(-\beta _{2}-\beta _{6})q^{5}-q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3844, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3844, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 2}\)