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

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

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

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