Properties

Label 546.4.a
Level $546$
Weight $4$
Character orbit 546.a
Rep. character $\chi_{546}(1,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $17$
Sturm bound $448$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(448\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(546))\).

Total New Old
Modular forms 344 36 308
Cusp forms 328 36 292
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.

\(2\)\(3\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(24\)
Minus space\(-\)\(12\)

Trace form

\( 36q + 144q^{4} + 324q^{9} + O(q^{10}) \) \( 36q + 144q^{4} + 324q^{9} + 576q^{16} + 256q^{17} + 160q^{19} + 84q^{21} + 144q^{22} + 144q^{23} + 1100q^{25} - 288q^{29} - 48q^{30} + 480q^{31} + 384q^{33} - 112q^{35} + 1296q^{36} - 432q^{37} + 544q^{38} + 1040q^{41} + 144q^{43} + 464q^{46} + 544q^{47} + 1764q^{49} + 1088q^{50} - 480q^{51} - 656q^{53} + 2336q^{55} + 1296q^{57} + 1328q^{58} - 880q^{59} + 592q^{61} + 64q^{62} + 2304q^{64} - 832q^{65} + 480q^{66} + 2664q^{67} + 1024q^{68} + 960q^{69} - 448q^{70} + 224q^{71} - 1888q^{73} + 1088q^{74} + 1920q^{75} + 640q^{76} + 312q^{78} + 2328q^{79} + 2916q^{81} - 1744q^{82} + 2592q^{83} + 336q^{84} + 4288q^{85} + 1216q^{86} - 1704q^{87} + 576q^{88} + 2208q^{89} + 364q^{91} + 576q^{92} + 768q^{93} + 2736q^{94} + 2488q^{95} + 784q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(546))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 13
546.4.a.a \(1\) \(32.215\) \(\Q\) None \(-2\) \(-3\) \(12\) \(7\) \(+\) \(+\) \(-\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+12q^{5}+6q^{6}+\cdots\)
546.4.a.b \(1\) \(32.215\) \(\Q\) None \(2\) \(-3\) \(-9\) \(7\) \(-\) \(+\) \(-\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-9q^{5}-6q^{6}+\cdots\)
546.4.a.c \(1\) \(32.215\) \(\Q\) None \(2\) \(3\) \(-14\) \(-7\) \(-\) \(-\) \(+\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}-14q^{5}+6q^{6}+\cdots\)
546.4.a.d \(1\) \(32.215\) \(\Q\) None \(2\) \(3\) \(-12\) \(7\) \(-\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}-12q^{5}+6q^{6}+\cdots\)
546.4.a.e \(1\) \(32.215\) \(\Q\) None \(2\) \(3\) \(9\) \(-7\) \(-\) \(-\) \(+\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+9q^{5}+6q^{6}+\cdots\)
546.4.a.f \(2\) \(32.215\) \(\Q(\sqrt{21}) \) None \(-4\) \(-6\) \(-8\) \(-14\) \(+\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(-4-\beta )q^{5}+\cdots\)
546.4.a.g \(2\) \(32.215\) \(\Q(\sqrt{65}) \) None \(-4\) \(6\) \(-15\) \(14\) \(+\) \(-\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(-8-\beta )q^{5}+\cdots\)
546.4.a.h \(2\) \(32.215\) \(\Q(\sqrt{129}) \) None \(-4\) \(6\) \(1\) \(-14\) \(+\) \(-\) \(+\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots\)
546.4.a.i \(2\) \(32.215\) \(\Q(\sqrt{673}) \) None \(-4\) \(6\) \(3\) \(-14\) \(+\) \(-\) \(+\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(1+\beta )q^{5}-6q^{6}+\cdots\)
546.4.a.j \(2\) \(32.215\) \(\Q(\sqrt{105}) \) None \(4\) \(-6\) \(5\) \(-14\) \(-\) \(+\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(3-\beta )q^{5}-6q^{6}+\cdots\)
546.4.a.k \(2\) \(32.215\) \(\Q(\sqrt{1401}) \) None \(4\) \(6\) \(5\) \(-14\) \(-\) \(-\) \(+\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(3-\beta )q^{5}+6q^{6}+\cdots\)
546.4.a.l \(3\) \(32.215\) 3.3.7441.1 None \(-6\) \(-9\) \(-6\) \(21\) \(+\) \(+\) \(-\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
546.4.a.m \(3\) \(32.215\) 3.3.1600113.1 None \(-6\) \(-9\) \(0\) \(-21\) \(+\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+\beta _{1}q^{5}+6q^{6}+\cdots\)
546.4.a.n \(3\) \(32.215\) 3.3.360321.1 None \(-6\) \(9\) \(13\) \(21\) \(+\) \(-\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(4-\beta _{2})q^{5}+\cdots\)
546.4.a.o \(3\) \(32.215\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(6\) \(-9\) \(-1\) \(21\) \(-\) \(+\) \(-\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}-\beta _{1}q^{5}-6q^{6}+\cdots\)
546.4.a.p \(3\) \(32.215\) 3.3.118088.1 None \(6\) \(-9\) \(7\) \(-21\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
546.4.a.q \(4\) \(32.215\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(12\) \(10\) \(28\) \(-\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(546))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(546)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)