Properties

Label 105.4.u
Level $105$
Weight $4$
Character orbit 105.u
Rep. character $\chi_{105}(52,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $96$
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.u (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
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 208 96 112
Cusp forms 176 96 80
Eisenstein series 32 0 32

Trace form

\( 96q + 48q^{5} - 4q^{7} + 168q^{8} + O(q^{10}) \) \( 96q + 48q^{5} - 4q^{7} + 168q^{8} - 72q^{10} + 56q^{11} - 168q^{15} + 880q^{16} + 96q^{21} + 624q^{22} - 64q^{23} + 152q^{25} + 912q^{26} + 628q^{28} + 48q^{30} - 528q^{31} - 672q^{32} - 108q^{33} - 1616q^{35} - 3456q^{36} - 552q^{37} - 4044q^{38} + 2052q^{40} - 1068q^{42} + 720q^{43} + 2560q^{46} + 240q^{47} - 3528q^{50} + 336q^{51} + 4644q^{52} + 1728q^{53} + 4896q^{56} + 1392q^{57} + 512q^{58} + 420q^{60} - 2592q^{61} - 288q^{63} - 824q^{65} - 4104q^{66} - 3784q^{67} - 8844q^{68} - 2256q^{70} - 128q^{71} - 756q^{72} - 3312q^{73} - 1872q^{75} - 6600q^{77} - 1200q^{78} + 12108q^{80} + 3888q^{81} + 6084q^{82} + 4768q^{85} - 1088q^{86} + 5652q^{87} + 4844q^{88} + 10128q^{91} - 2152q^{92} + 1368q^{93} - 7872q^{95} + 20184q^{98} + O(q^{100}) \)

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.u.a \(96\) \(6.195\) None \(0\) \(0\) \(48\) \(-4\)

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

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