Properties

Label 2563.1.b
Level 2563
Weight 1
Character orbit b
Rep. character \(\chi_{2563}(2562,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 4
Sturm bound 234
Trace bound 11

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Defining parameters

Level: \( N \) = \( 2563 = 11 \cdot 233 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2563.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 2563 \)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(234\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2563, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 4 0

Trace form

\( 6q - 2q^{4} - 2q^{9} + O(q^{10}) \) \( 6q - 2q^{4} - 2q^{9} + 8q^{15} - 2q^{16} - 6q^{23} - 2q^{25} - 6q^{31} + 6q^{36} + 2q^{37} - 8q^{38} + 6q^{49} - 8q^{58} - 8q^{60} + 6q^{64} - 8q^{66} - 6q^{71} - 2q^{81} + 2q^{89} + 2q^{92} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2563, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2563.1.b.a \(1\) \(1.279\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2563}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-q^{11}+q^{16}+q^{17}-q^{23}+\cdots\)
2563.1.b.b \(1\) \(1.279\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-2563}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}+q^{11}+q^{16}-q^{17}-q^{23}+\cdots\)
2563.1.b.c \(2\) \(1.279\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-\beta q^{3}-q^{4}+\beta q^{5}-2q^{6}+\cdots\)
2563.1.b.d \(2\) \(1.279\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+\beta q^{3}-q^{4}-\beta q^{5}+2q^{6}+\cdots\)