Properties

Label 105.4.j
Level $105$
Weight $4$
Character orbit 105.j
Rep. character $\chi_{105}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 104 72 32
Cusp forms 88 72 16
Eisenstein series 16 0 16

Trace form

\( 72q + 8q^{3} + O(q^{10}) \) \( 72q + 8q^{3} + 144q^{10} - 128q^{12} - 144q^{13} - 16q^{15} - 1608q^{16} + 460q^{18} + 112q^{21} + 576q^{22} + 504q^{25} - 592q^{27} - 580q^{30} - 960q^{31} - 56q^{33} + 928q^{36} + 2088q^{37} + 144q^{40} - 140q^{42} + 240q^{43} - 880q^{45} + 528q^{46} + 3208q^{48} + 1960q^{51} + 240q^{52} + 1200q^{55} - 1112q^{57} + 840q^{58} - 1528q^{60} - 1824q^{61} - 1064q^{63} - 1408q^{66} - 2832q^{67} - 1008q^{70} - 296q^{72} + 1776q^{73} + 5280q^{75} + 7296q^{76} - 4500q^{78} - 4064q^{81} + 1680q^{82} - 10536q^{85} - 392q^{87} - 5352q^{88} - 5664q^{90} + 1008q^{91} - 5488q^{93} - 288q^{96} - 7872q^{97} + O(q^{100}) \)

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.j.a \(72\) \(6.195\) None \(0\) \(8\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)