Properties

Label 105.2.g
Level 105
Weight 2
Character orbit g
Rep. character \(\chi_{105}(104,\cdot)\)
Character field \(\Q\)
Dimension 12
Newforms 3
Sturm bound 32
Trace bound 3

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

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

Trace form

\(12q \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 6q^{21} \) \(\mathstrut -\mathstrut 12q^{25} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 18q^{39} \) \(\mathstrut +\mathstrut 48q^{46} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut +\mathstrut 42q^{51} \) \(\mathstrut +\mathstrut 36q^{60} \) \(\mathstrut -\mathstrut 24q^{64} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 60q^{79} \) \(\mathstrut -\mathstrut 90q^{81} \) \(\mathstrut -\mathstrut 36q^{84} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 60q^{91} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.2.g.a \(4\) \(0.838\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(-4\) \(0\) \(4\) \(q-\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
105.2.g.b \(4\) \(0.838\) \(\Q(\sqrt{-5}, \sqrt{7})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-2q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
105.2.g.c \(4\) \(0.838\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(4\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)