Properties

Label 354.4.a
Level 354
Weight 4
Character orbit a
Rep. character \(\chi_{354}(1,\cdot)\)
Character field \(\Q\)
Dimension 28
Newform subspaces 9
Sturm bound 240
Trace bound 5

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 354.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(240\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(354))\).

Total New Old
Modular forms 184 28 156
Cusp forms 176 28 148
Eisenstein series 8 0 8

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

\(2\)\(3\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(18\)
Minus space\(-\)\(10\)

Trace form

\( 28q + 4q^{2} + 6q^{3} + 112q^{4} - 12q^{5} + 44q^{7} + 16q^{8} + 252q^{9} + O(q^{10}) \) \( 28q + 4q^{2} + 6q^{3} + 112q^{4} - 12q^{5} + 44q^{7} + 16q^{8} + 252q^{9} + 40q^{10} + 112q^{11} + 24q^{12} + 8q^{13} - 48q^{15} + 448q^{16} + 324q^{17} + 36q^{18} - 96q^{19} - 48q^{20} - 96q^{21} - 232q^{22} - 208q^{23} + 1268q^{25} - 152q^{26} + 54q^{27} + 176q^{28} + 12q^{29} + 48q^{30} + 68q^{31} + 64q^{32} + 192q^{33} + 152q^{34} + 104q^{35} + 1008q^{36} - 544q^{37} + 208q^{38} + 252q^{39} + 160q^{40} - 356q^{41} + 92q^{43} + 448q^{44} - 108q^{45} + 64q^{46} + 584q^{47} + 96q^{48} + 1560q^{49} - 580q^{50} + 36q^{51} + 32q^{52} - 412q^{53} + 1584q^{55} + 888q^{57} + 136q^{58} - 192q^{60} + 3608q^{61} + 32q^{62} + 396q^{63} + 1792q^{64} + 1848q^{65} - 768q^{66} - 332q^{67} + 1296q^{68} + 1248q^{69} + 144q^{70} + 1864q^{71} + 144q^{72} + 1664q^{73} + 1688q^{74} + 426q^{75} - 384q^{76} + 1496q^{77} - 312q^{78} - 1748q^{79} - 192q^{80} + 2268q^{81} + 648q^{82} - 1288q^{83} - 384q^{84} + 1752q^{85} + 48q^{86} + 1152q^{87} - 928q^{88} - 5468q^{89} + 360q^{90} + 1392q^{91} - 832q^{92} + 36q^{93} - 2672q^{94} - 4768q^{95} - 2336q^{97} - 860q^{98} + 1008q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(354))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 59
354.4.a.a \(2\) \(20.887\) \(\Q(\sqrt{21}) \) None \(-4\) \(6\) \(-12\) \(-23\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(-5-2\beta )q^{5}+\cdots\)
354.4.a.b \(2\) \(20.887\) \(\Q(\sqrt{51}) \) None \(-4\) \(6\) \(26\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(13+\beta )q^{5}+\cdots\)
354.4.a.c \(2\) \(20.887\) \(\Q(\sqrt{13}) \) None \(4\) \(6\) \(-20\) \(-23\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(-9-2\beta )q^{5}+\cdots\)
354.4.a.d \(3\) \(20.887\) 3.3.30645.1 None \(-6\) \(-9\) \(-6\) \(6\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+(-2-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
354.4.a.e \(3\) \(20.887\) 3.3.45581.1 None \(-6\) \(-9\) \(4\) \(13\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.f \(3\) \(20.887\) 3.3.18989.1 None \(-6\) \(9\) \(-28\) \(26\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(-9+\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.g \(3\) \(20.887\) 3.3.47277.1 None \(6\) \(-9\) \(-18\) \(6\) \(-\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(-6+\beta _{1}+\beta _{2})q^{5}+\cdots\)
354.4.a.h \(4\) \(20.887\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(-12\) \(22\) \(13\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+(5+\beta _{1}-\beta _{3})q^{5}+\cdots\)
354.4.a.i \(6\) \(20.887\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(18\) \(20\) \(26\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(354))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(354)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 2}\)