Properties

Label 1800.1.bk
Level 1800
Weight 1
Character orbit bk
Rep. character \(\chi_{1800}(1051,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 10
Newforms 5
Sturm bound 360
Trace bound 6

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1800.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 5 \)
Sturm bound: \(360\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1800, [\chi])\).

Total New Old
Modular forms 40 22 18
Cusp forms 16 10 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 10 0 0 0

Trace form

\( 10q + q^{2} + q^{3} - 5q^{4} + q^{6} - 2q^{8} + q^{9} + O(q^{10}) \) \( 10q + q^{2} + q^{3} - 5q^{4} + q^{6} - 2q^{8} + q^{9} - q^{11} - 2q^{12} - 5q^{16} + 2q^{17} - 2q^{18} + 2q^{19} - q^{22} + q^{24} - 2q^{27} + q^{32} - q^{33} - q^{34} + q^{36} - q^{38} - q^{41} - q^{43} + 2q^{44} + q^{48} - 5q^{49} + 11q^{51} - 5q^{54} - q^{57} + 5q^{59} + 10q^{64} - 4q^{66} - q^{67} - q^{68} + q^{72} + 2q^{73} - q^{76} + q^{81} + 2q^{82} + 2q^{83} + 5q^{86} - q^{88} - 4q^{89} - 2q^{96} - q^{97} - 2q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1800.1.bk.a \(2\) \(0.898\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}+q^{8}+\cdots\)
1800.1.bk.b \(2\) \(0.898\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(-1\) \(2\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\)
1800.1.bk.c \(2\) \(0.898\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(1\) \(-2\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{6}+\cdots\)
1800.1.bk.d \(2\) \(0.898\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
1800.1.bk.e \(2\) \(0.898\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-2}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}-q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)