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Properties

Label 3800.1.bd
Level $3800$
Weight $1$
Character orbit 3800.bd
Rep. character $\chi_{3800}(1451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
Newform subspaces $6$
Sturm bound $600$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3800.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(600\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3800, [\chi])\).

Total New Old
Modular forms 44 26 18
Cusp forms 20 14 6
Eisenstein series 24 12 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14 q + q^{2} - q^{3} - 3 q^{4} - q^{6} - 2 q^{8} - 4 q^{9} + O(q^{10}) \) \( 14 q + q^{2} - q^{3} - 3 q^{4} - q^{6} - 2 q^{8} - 4 q^{9} - 2 q^{11} + 2 q^{12} - 2 q^{14} - 7 q^{16} + 2 q^{17} + 3 q^{19} - q^{22} - q^{24} + 8 q^{26} - 2 q^{27} + q^{32} + q^{33} + 2 q^{34} - 8 q^{36} - 2 q^{38} + q^{41} + 2 q^{43} - 3 q^{44} - 4 q^{46} - q^{48} + 10 q^{49} + 4 q^{51} - 11 q^{54} - 4 q^{56} + 2 q^{57} + 9 q^{59} + 6 q^{64} + 7 q^{66} - q^{67} - 4 q^{68} - q^{73} - 2 q^{74} + 5 q^{76} - 9 q^{81} - q^{82} + 2 q^{83} - 10 q^{86} + 2 q^{88} + 4 q^{91} - 8 q^{94} + 2 q^{96} - q^{97} + q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3800.1.bd.a 3800.bd 152.k $2$ $1.896$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots\)
3800.1.bd.b 3800.bd 152.k $2$ $1.896$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.c 3800.bd 152.k $2$ $1.896$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.d 3800.bd 152.k $2$ $1.896$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
3800.1.bd.e 3800.bd 152.k $2$ $1.896$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) None \(1\) \(2\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots\)
3800.1.bd.f 3800.bd 152.k $4$ $1.896$ \(\Q(\zeta_{12})\) $D_{3}$ \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3800, [\chi]) \cong \)