Properties

Label 147.4.e
Level $147$
Weight $4$
Character orbit 147.e
Rep. character $\chi_{147}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $14$
Sturm bound $74$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(74\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(147, [\chi])\).

Total New Old
Modular forms 128 40 88
Cusp forms 96 40 56
Eisenstein series 32 0 32

Trace form

\( 40q - 4q^{2} - 6q^{3} - 60q^{4} + 8q^{5} + 24q^{6} - 156q^{8} - 180q^{9} + O(q^{10}) \) \( 40q - 4q^{2} - 6q^{3} - 60q^{4} + 8q^{5} + 24q^{6} - 156q^{8} - 180q^{9} - 46q^{10} + 40q^{11} - 72q^{12} + 4q^{13} + 84q^{15} - 164q^{16} + 132q^{17} - 36q^{18} - 218q^{19} - 872q^{20} - 180q^{22} + 208q^{23} - 54q^{24} - 686q^{25} + 466q^{26} + 108q^{27} + 920q^{29} + 216q^{30} - 348q^{31} + 1050q^{32} - 150q^{33} + 552q^{34} + 1080q^{36} + 550q^{37} - 350q^{38} + 42q^{39} - 42q^{40} - 1208q^{41} - 2076q^{43} - 1112q^{44} + 72q^{45} - 1076q^{46} - 240q^{47} + 1872q^{48} - 920q^{50} + 48q^{51} + 260q^{52} + 2884q^{53} - 108q^{54} + 1972q^{55} - 1140q^{57} + 418q^{58} + 1128q^{59} - 1938q^{60} - 188q^{61} - 3636q^{62} + 2664q^{64} - 336q^{65} + 156q^{66} - 2290q^{67} + 2028q^{68} + 1800q^{69} + 376q^{71} + 702q^{72} + 1350q^{73} + 1534q^{74} - 738q^{75} + 4712q^{76} - 108q^{78} + 248q^{79} + 388q^{80} - 1620q^{81} - 956q^{82} - 1992q^{83} + 2264q^{85} + 4670q^{86} - 1050q^{87} + 6198q^{88} + 2672q^{89} + 828q^{90} - 10360q^{92} - 3006q^{93} - 3204q^{94} - 928q^{95} - 1914q^{96} - 1044q^{97} - 720q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
147.4.e.a \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(-3\) \(-18\) \(0\) \(q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.b \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(-3\) \(-4\) \(0\) \(q-4\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.c \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(3\) \(4\) \(0\) \(q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.d \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(-4\) \(3\) \(18\) \(0\) \(q-4\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.e.e \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(12\) \(0\) \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
147.4.e.f \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-12\) \(0\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
147.4.e.g \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(3\) \(-3\) \(-18\) \(0\) \(q+3\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.h \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(-3\) \(0\) \(q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.i \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) None \(3\) \(3\) \(18\) \(0\) \(q+3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
147.4.e.j \(4\) \(8.673\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-6\) \(20\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.k \(4\) \(8.673\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(6\) \(-20\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}-3\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.l \(4\) \(8.673\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(3\) \(-6\) \(-6\) \(0\) \(q+(1+\beta _{1}+\beta _{3})q^{2}+3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.m \(4\) \(8.673\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(3\) \(6\) \(6\) \(0\) \(q+(1+\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(7\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.e.n \(6\) \(8.673\) 6.0.9924270768.1 None \(-1\) \(-9\) \(11\) \(0\) \(q-\beta _{1}q^{2}+(-3+3\beta _{4})q^{3}+(-8+\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)