Properties

Label 147.4.a
Level $147$
Weight $4$
Character orbit 147.a
Rep. character $\chi_{147}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $13$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(74\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(147))\).

Total New Old
Modular forms 64 20 44
Cusp forms 48 20 28
Eisenstein series 16 0 16

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(12\)
Minus space\(-\)\(8\)

Trace form

\( 20q + 4q^{2} + 60q^{4} + 16q^{5} + 12q^{6} + 48q^{8} + 180q^{9} + O(q^{10}) \) \( 20q + 4q^{2} + 60q^{4} + 16q^{5} + 12q^{6} + 48q^{8} + 180q^{9} + 28q^{10} - 40q^{11} - 24q^{12} + 80q^{13} - 84q^{15} + 332q^{16} - 120q^{17} + 36q^{18} - 40q^{19} - 172q^{20} - 132q^{22} - 40q^{23} + 324q^{24} + 728q^{25} - 172q^{26} + 376q^{29} + 288q^{30} + 168q^{31} + 168q^{32} + 96q^{33} - 276q^{34} + 540q^{36} - 508q^{37} - 1360q^{38} - 756q^{39} + 924q^{40} + 1016q^{41} - 828q^{43} - 1072q^{44} + 144q^{45} - 520q^{46} - 552q^{47} - 816q^{48} - 292q^{50} + 456q^{51} + 1420q^{52} - 784q^{53} + 108q^{54} - 952q^{55} - 276q^{57} - 124q^{58} - 792q^{59} - 204q^{60} - 592q^{61} + 1824q^{62} + 156q^{64} - 168q^{65} + 1896q^{66} + 148q^{67} - 492q^{68} - 144q^{69} + 608q^{71} + 432q^{72} + 72q^{73} + 1196q^{74} + 624q^{75} + 832q^{76} - 1692q^{78} + 1936q^{79} - 3484q^{80} + 1620q^{81} - 1492q^{82} - 2208q^{83} + 3904q^{85} - 9836q^{86} + 1032q^{87} - 5484q^{88} - 920q^{89} + 252q^{90} - 2744q^{92} + 1788q^{93} + 1344q^{94} - 416q^{95} + 204q^{96} + 744q^{97} - 360q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(147))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7
147.4.a.a \(1\) \(8.673\) \(\Q\) None \(-3\) \(-3\) \(3\) \(0\) \(+\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}+3q^{5}+9q^{6}+\cdots\)
147.4.a.b \(1\) \(8.673\) \(\Q\) None \(-3\) \(3\) \(-3\) \(0\) \(-\) \(+\) \(q-3q^{2}+3q^{3}+q^{4}-3q^{5}-9q^{6}+\cdots\)
147.4.a.c \(1\) \(8.673\) \(\Q\) None \(-3\) \(3\) \(18\) \(0\) \(-\) \(-\) \(q-3q^{2}+3q^{3}+q^{4}+18q^{5}-9q^{6}+\cdots\)
147.4.a.d \(1\) \(8.673\) \(\Q\) None \(-1\) \(-3\) \(12\) \(0\) \(+\) \(-\) \(q-q^{2}-3q^{3}-7q^{4}+12q^{5}+3q^{6}+\cdots\)
147.4.a.e \(1\) \(8.673\) \(\Q\) None \(-1\) \(3\) \(-12\) \(0\) \(-\) \(-\) \(q-q^{2}+3q^{3}-7q^{4}-12q^{5}-3q^{6}+\cdots\)
147.4.a.f \(1\) \(8.673\) \(\Q\) None \(4\) \(-3\) \(-18\) \(0\) \(+\) \(-\) \(q+4q^{2}-3q^{3}+8q^{4}-18q^{5}-12q^{6}+\cdots\)
147.4.a.g \(1\) \(8.673\) \(\Q\) None \(4\) \(3\) \(4\) \(0\) \(-\) \(-\) \(q+4q^{2}+3q^{3}+8q^{4}+4q^{5}+12q^{6}+\cdots\)
147.4.a.h \(1\) \(8.673\) \(\Q\) None \(4\) \(3\) \(18\) \(0\) \(-\) \(-\) \(q+4q^{2}+3q^{3}+8q^{4}+18q^{5}+12q^{6}+\cdots\)
147.4.a.i \(2\) \(8.673\) \(\Q(\sqrt{57}) \) None \(-3\) \(-6\) \(-6\) \(0\) \(+\) \(-\) \(q+(-1-\beta )q^{2}-3q^{3}+(7+3\beta )q^{4}+\cdots\)
147.4.a.j \(2\) \(8.673\) \(\Q(\sqrt{2}) \) None \(2\) \(-6\) \(20\) \(0\) \(+\) \(+\) \(q+(1+\beta )q^{2}-3q^{3}+(-5+2\beta )q^{4}+\cdots\)
147.4.a.k \(2\) \(8.673\) \(\Q(\sqrt{2}) \) None \(2\) \(6\) \(-20\) \(0\) \(-\) \(+\) \(q+(1+\beta )q^{2}+3q^{3}+(-5+2\beta )q^{4}+\cdots\)
147.4.a.l \(3\) \(8.673\) 3.3.57516.1 None \(1\) \(-9\) \(11\) \(0\) \(+\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(8+\beta _{1}+\beta _{2})q^{4}+\cdots\)
147.4.a.m \(3\) \(8.673\) 3.3.57516.1 None \(1\) \(9\) \(-11\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{2}+3q^{3}+(8+\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(147))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(147)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)