Properties

Label 147.4.g
Level $147$
Weight $4$
Character orbit 147.g
Rep. character $\chi_{147}(68,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $5$
Sturm bound $74$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

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

Total New Old
Modular forms 128 88 40
Cusp forms 96 72 24
Eisenstein series 32 16 16

Trace form

\( 72 q + 3 q^{3} + 130 q^{4} + 19 q^{9} + O(q^{10}) \) \( 72 q + 3 q^{3} + 130 q^{4} + 19 q^{9} - 30 q^{10} + 192 q^{12} + 110 q^{15} - 638 q^{16} - 106 q^{18} - 300 q^{19} + 52 q^{22} - 414 q^{24} - 444 q^{25} + 1086 q^{30} + 930 q^{31} + 855 q^{33} - 572 q^{36} - 368 q^{37} + 1018 q^{39} - 2298 q^{40} + 172 q^{43} - 2367 q^{45} - 1640 q^{46} + 2043 q^{51} + 3000 q^{52} + 4158 q^{54} + 734 q^{57} - 4466 q^{58} + 3078 q^{60} - 2358 q^{61} - 460 q^{64} - 2934 q^{66} - 984 q^{67} + 4964 q^{72} + 2904 q^{73} + 2418 q^{75} - 592 q^{78} - 1110 q^{79} - 345 q^{81} - 5040 q^{82} - 2244 q^{85} - 1638 q^{87} + 614 q^{88} + 2125 q^{93} + 1356 q^{94} + 4410 q^{96} - 3978 q^{99} + O(q^{100}) \)

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.g.a \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(0\) \(q+(-3-3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
147.4.g.b \(2\) \(8.673\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(0\) \(q+(3+3\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+3^{3}\zeta_{6}q^{9}+\cdots\)
147.4.g.c \(8\) \(8.673\) 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(-\beta _{5}-\beta _{7})q^{3}+(9-9\beta _{1}+\cdots)q^{4}+\cdots\)
147.4.g.d \(12\) \(8.673\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{6})q^{2}+(-\beta _{7}-\beta _{8})q^{3}+(-2\beta _{4}+\cdots)q^{4}+\cdots\)
147.4.g.e \(48\) \(8.673\) None \(0\) \(0\) \(0\) \(0\)

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

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