Properties

Label 105.4.m
Level $105$
Weight $4$
Character orbit 105.m
Rep. character $\chi_{105}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 48 56
Cusp forms 88 48 40
Eisenstein series 16 0 16

Trace form

\( 48q + 4q^{7} - 168q^{8} + O(q^{10}) \) \( 48q + 4q^{7} - 168q^{8} + 112q^{11} + 168q^{15} - 544q^{16} - 96q^{21} - 192q^{22} + 400q^{23} + 520q^{25} + 1052q^{28} - 48q^{30} - 1344q^{32} + 392q^{35} - 1728q^{36} - 456q^{37} + 1068q^{42} + 192q^{43} - 208q^{46} + 3528q^{50} + 672q^{51} - 1728q^{53} - 48q^{56} + 696q^{57} + 3016q^{58} + 840q^{60} - 36q^{63} - 4720q^{65} - 4784q^{67} + 2220q^{70} - 3088q^{71} - 1512q^{72} + 2352q^{77} + 1416q^{78} - 3888q^{81} - 472q^{85} + 10832q^{86} + 2128q^{88} - 5664q^{91} + 10600q^{92} - 1368q^{93} - 6912q^{95} - 3888q^{98} + O(q^{100}) \)

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.m.a \(48\) \(6.195\) None \(0\) \(0\) \(0\) \(4\)

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

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)