Properties

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

Related objects

Downloads

Learn more

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: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1800.1.bk.a 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) 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 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) 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 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) 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 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) 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 1800.bk 72.p $2$ $0.898$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-2}) \) 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

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