Properties

Label 717.4.a
Level $717$
Weight $4$
Character orbit 717.a
Rep. character $\chi_{717}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $4$
Sturm bound $320$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 717 = 3 \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 717.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(320\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(717))\).

Total New Old
Modular forms 242 120 122
Cusp forms 238 120 118
Eisenstein series 4 0 4

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

\(3\)\(239\)FrickeDim.
\(+\)\(+\)\(+\)\(32\)
\(+\)\(-\)\(-\)\(28\)
\(-\)\(+\)\(-\)\(28\)
\(-\)\(-\)\(+\)\(32\)
Plus space\(+\)\(64\)
Minus space\(-\)\(56\)

Trace form

\( 120q - 4q^{2} + 500q^{4} - 16q^{5} - 20q^{7} + 36q^{8} + 1080q^{9} + O(q^{10}) \) \( 120q - 4q^{2} + 500q^{4} - 16q^{5} - 20q^{7} + 36q^{8} + 1080q^{9} - 72q^{10} + 56q^{11} - 24q^{12} - 68q^{13} + 60q^{14} + 2092q^{16} + 152q^{17} - 36q^{18} - 152q^{19} - 636q^{20} - 84q^{21} + 172q^{22} + 320q^{23} + 3152q^{25} - 520q^{26} - 824q^{28} - 344q^{29} + 120q^{30} - 96q^{31} + 844q^{32} - 96q^{33} - 144q^{34} + 320q^{35} + 4500q^{36} - 332q^{37} - 592q^{38} - 312q^{39} - 612q^{40} - 8q^{41} - 828q^{42} - 424q^{43} - 660q^{44} - 144q^{45} - 712q^{46} - 672q^{47} + 336q^{48} + 6416q^{49} - 1616q^{50} - 336q^{51} - 1552q^{52} + 128q^{53} + 880q^{55} - 1392q^{56} + 84q^{57} - 360q^{58} + 112q^{59} - 804q^{60} - 864q^{61} + 2044q^{62} - 180q^{63} + 8596q^{64} + 352q^{65} + 1032q^{66} + 80q^{67} + 5436q^{68} - 696q^{69} + 1888q^{70} + 1480q^{71} + 324q^{72} - 1192q^{73} - 2208q^{74} + 624q^{75} - 544q^{76} + 1944q^{77} - 384q^{78} - 2148q^{79} - 3392q^{80} + 9720q^{81} + 5472q^{82} - 1336q^{83} + 1248q^{84} - 2328q^{85} - 1192q^{86} + 120q^{87} - 380q^{88} - 912q^{89} - 648q^{90} + 2192q^{91} + 8812q^{92} - 1056q^{93} + 2892q^{94} - 3072q^{95} + 2580q^{96} - 1544q^{97} - 5832q^{98} + 504q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(717))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 239
717.4.a.a \(28\) \(42.304\) None \(-13\) \(84\) \(-74\) \(-82\) \(-\) \(+\)
717.4.a.b \(28\) \(42.304\) None \(-5\) \(-84\) \(6\) \(-68\) \(+\) \(-\)
717.4.a.c \(32\) \(42.304\) None \(3\) \(-96\) \(-14\) \(72\) \(+\) \(+\)
717.4.a.d \(32\) \(42.304\) None \(11\) \(96\) \(66\) \(58\) \(-\) \(-\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(717))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(717)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(239))\)\(^{\oplus 2}\)