Properties

Label 105.4.g
Level $105$
Weight $4$
Character orbit 105.g
Rep. character $\chi_{105}(104,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44q + 152q^{4} - 48q^{9} + O(q^{10}) \) \( 44q + 152q^{4} - 48q^{9} + 12q^{15} + 440q^{16} - 48q^{21} + 212q^{25} - 336q^{30} - 1104q^{36} - 252q^{39} - 1488q^{46} - 124q^{49} + 1620q^{51} + 384q^{60} - 2008q^{64} - 3000q^{70} - 248q^{79} + 3072q^{81} - 624q^{84} + 208q^{85} + 1864q^{91} + 6396q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.4.g.a \(4\) \(6.195\) \(\Q(\sqrt{-5}, \sqrt{7})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{3})q^{3}-8q^{4}-5\beta _{1}q^{5}+7\beta _{3}q^{7}+\cdots\)
105.4.g.b \(40\) \(6.195\) None \(0\) \(0\) \(0\) \(0\)