Properties

Label 633.1.m
Level 633
Weight 1
Character orbit m
Rep. character \(\chi_{633}(71,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 12
Newforms 2
Sturm bound 70
Trace bound 1

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Defining parameters

Level: \( N \) = \( 633 = 3 \cdot 211 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 633.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 633 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 2 \)
Sturm bound: \(70\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(633, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 8

Trace form

\(12q \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut -\mathstrut 5q^{4} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut +\mathstrut q^{19} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 5q^{36} \) \(\mathstrut +\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut +\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut +\mathstrut 9q^{76} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 3q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 3q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 7q^{93} \) \(\mathstrut -\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(633, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
633.1.m.a \(4\) \(0.316\) \(\Q(\zeta_{10})\) \(D_{5}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(3\) \(q-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
633.1.m.b \(8\) \(0.316\) \(\Q(\zeta_{20})\) \(A_{5}\) None None \(0\) \(2\) \(0\) \(-2\) \(q+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)