Properties

Label 1800.1.dg
Level 1800
Weight 1
Character orbit dg
Rep. character \(\chi_{1800}(211,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 16
Newforms 1
Sturm bound 360
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 1800.dg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1800 \)
Character field: \(\Q(\zeta_{30})\)
Newforms: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 0 16

Trace form

\(16q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 16q^{30} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 2q^{42} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{56} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut -\mathstrut 4q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.dg.a \(16\) \(0.898\) \(\Q(\zeta_{60})\) \(A_{5}\) None None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{60}^{29}q^{2}+\zeta_{60}^{18}q^{3}-\zeta_{60}^{28}q^{4}+\cdots\)