Properties

Label 105.4.i
Level $105$
Weight $4$
Character orbit 105.i
Rep. character $\chi_{105}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $5$
Sturm bound $64$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32q - 4q^{2} - 12q^{3} - 44q^{4} + 44q^{7} - 72q^{8} - 144q^{9} + O(q^{10}) \) \( 32q - 4q^{2} - 12q^{3} - 44q^{4} + 44q^{7} - 72q^{8} - 144q^{9} - 40q^{10} + 68q^{11} - 144q^{12} + 8q^{13} + 136q^{14} - 100q^{16} + 8q^{17} - 36q^{18} - 136q^{19} + 80q^{20} - 168q^{21} - 776q^{22} + 328q^{23} + 180q^{24} - 400q^{25} + 716q^{26} + 216q^{27} - 768q^{28} + 1136q^{29} + 92q^{31} + 784q^{32} - 264q^{33} - 448q^{34} + 220q^{35} + 792q^{36} - 660q^{37} - 56q^{38} - 588q^{39} - 480q^{40} - 1016q^{41} + 564q^{42} - 376q^{43} + 368q^{44} - 1180q^{46} + 368q^{47} + 2688q^{48} + 252q^{49} + 200q^{50} + 48q^{51} - 908q^{52} + 2152q^{53} + 1520q^{55} + 588q^{56} - 840q^{57} + 2196q^{58} + 1376q^{59} + 2272q^{61} - 6360q^{62} - 36q^{63} + 424q^{64} - 420q^{65} + 684q^{66} - 228q^{67} - 2988q^{68} + 1296q^{69} - 3020q^{70} - 3008q^{71} + 324q^{72} - 972q^{73} + 976q^{74} - 300q^{75} + 3944q^{76} + 2560q^{77} + 2472q^{78} + 1076q^{79} - 320q^{80} - 1296q^{81} + 332q^{82} - 2288q^{83} - 60q^{84} + 1120q^{85} - 6428q^{86} - 2088q^{87} + 232q^{88} + 2072q^{89} + 720q^{90} + 2468q^{91} - 5912q^{92} + 420q^{93} - 3292q^{94} + 600q^{95} + 1440q^{96} - 1440q^{97} - 3168q^{98} - 1224q^{99} + O(q^{100}) \)

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.i.a \(2\) \(6.195\) \(\Q(\sqrt{-3}) \) None \(-3\) \(3\) \(5\) \(-28\) \(q-3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
105.4.i.b \(4\) \(6.195\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(6\) \(10\) \(50\) \(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{2}+(3+3\beta _{2}+\cdots)q^{3}+\cdots\)
105.4.i.c \(6\) \(6.195\) 6.0.646154928.2 None \(-3\) \(9\) \(-15\) \(-2\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(3-3\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
105.4.i.d \(10\) \(6.195\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-15\) \(-25\) \(-32\) \(q+(\beta _{1}+\beta _{4})q^{2}+(-3-3\beta _{4})q^{3}+(-5+\cdots)q^{4}+\cdots\)
105.4.i.e \(10\) \(6.195\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-15\) \(25\) \(56\) \(q+\beta _{1}q^{2}-3\beta _{4}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)