Properties

Label 105.2.g
Level $105$
Weight $2$
Character orbit 105.g
Rep. character $\chi_{105}(104,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
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: \(\Q\)
Newform subspaces: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

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 \(0\) \(4\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)