Properties

Label 5.20.a
Level 5
Weight 20
Character orbit a
Rep. character \(\chi_{5}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 2
Sturm bound 10
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 5.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(5))\).

Total New Old
Modular forms 11 7 4
Cusp forms 9 7 2
Eisenstein series 2 0 2

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

\(5\)Dim.
\(+\)\(4\)
\(-\)\(3\)

Trace form

\(7q \) \(\mathstrut -\mathstrut 1426q^{2} \) \(\mathstrut -\mathstrut 70372q^{3} \) \(\mathstrut +\mathstrut 3039876q^{4} \) \(\mathstrut -\mathstrut 1953125q^{5} \) \(\mathstrut -\mathstrut 4615256q^{6} \) \(\mathstrut +\mathstrut 159110944q^{7} \) \(\mathstrut -\mathstrut 432759000q^{8} \) \(\mathstrut +\mathstrut 1563941539q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 1426q^{2} \) \(\mathstrut -\mathstrut 70372q^{3} \) \(\mathstrut +\mathstrut 3039876q^{4} \) \(\mathstrut -\mathstrut 1953125q^{5} \) \(\mathstrut -\mathstrut 4615256q^{6} \) \(\mathstrut +\mathstrut 159110944q^{7} \) \(\mathstrut -\mathstrut 432759000q^{8} \) \(\mathstrut +\mathstrut 1563941539q^{9} \) \(\mathstrut -\mathstrut 1144531250q^{10} \) \(\mathstrut +\mathstrut 3018769244q^{11} \) \(\mathstrut +\mathstrut 34268935264q^{12} \) \(\mathstrut -\mathstrut 70818176502q^{13} \) \(\mathstrut +\mathstrut 80868226272q^{14} \) \(\mathstrut -\mathstrut 149476562500q^{15} \) \(\mathstrut +\mathstrut 1546936336272q^{16} \) \(\mathstrut +\mathstrut 936291665534q^{17} \) \(\mathstrut -\mathstrut 5809160185642q^{18} \) \(\mathstrut +\mathstrut 3260177785140q^{19} \) \(\mathstrut -\mathstrut 2207242187500q^{20} \) \(\mathstrut +\mathstrut 4718266467504q^{21} \) \(\mathstrut +\mathstrut 849947048408q^{22} \) \(\mathstrut -\mathstrut 22481077696032q^{23} \) \(\mathstrut +\mathstrut 12711449598720q^{24} \) \(\mathstrut +\mathstrut 26702880859375q^{25} \) \(\mathstrut -\mathstrut 51856456051516q^{26} \) \(\mathstrut -\mathstrut 115566788254600q^{27} \) \(\mathstrut +\mathstrut 167911647644272q^{28} \) \(\mathstrut +\mathstrut 42986965257610q^{29} \) \(\mathstrut +\mathstrut 217828609375000q^{30} \) \(\mathstrut -\mathstrut 33476462030096q^{31} \) \(\mathstrut -\mathstrut 337349702226656q^{32} \) \(\mathstrut +\mathstrut 305281220352976q^{33} \) \(\mathstrut -\mathstrut 368189728088068q^{34} \) \(\mathstrut -\mathstrut 525257531250000q^{35} \) \(\mathstrut +\mathstrut 2990506101983252q^{36} \) \(\mathstrut -\mathstrut 379142637557086q^{37} \) \(\mathstrut -\mathstrut 3622228763368600q^{38} \) \(\mathstrut -\mathstrut 2685610971477112q^{39} \) \(\mathstrut -\mathstrut 1164520546875000q^{40} \) \(\mathstrut +\mathstrut 7687655590916134q^{41} \) \(\mathstrut -\mathstrut 8272493269099632q^{42} \) \(\mathstrut +\mathstrut 5024194115931108q^{43} \) \(\mathstrut +\mathstrut 7906770871289392q^{44} \) \(\mathstrut +\mathstrut 2452758677734375q^{45} \) \(\mathstrut -\mathstrut 15966760234147776q^{46} \) \(\mathstrut -\mathstrut 10457356780286296q^{47} \) \(\mathstrut +\mathstrut 36267409908976768q^{48} \) \(\mathstrut +\mathstrut 29290928428639951q^{49} \) \(\mathstrut -\mathstrut 5439758300781250q^{50} \) \(\mathstrut -\mathstrut 33120574104447176q^{51} \) \(\mathstrut -\mathstrut 101380328345593576q^{52} \) \(\mathstrut +\mathstrut 1553621744917778q^{53} \) \(\mathstrut +\mathstrut 157924438603485040q^{54} \) \(\mathstrut -\mathstrut 39360656820312500q^{55} \) \(\mathstrut +\mathstrut 11366910416633760q^{56} \) \(\mathstrut -\mathstrut 43866844325023600q^{57} \) \(\mathstrut -\mathstrut 35466560455978700q^{58} \) \(\mathstrut +\mathstrut 189158980318403420q^{59} \) \(\mathstrut -\mathstrut 345683170812500000q^{60} \) \(\mathstrut +\mathstrut 207691291189459194q^{61} \) \(\mathstrut -\mathstrut 661293594985584672q^{62} \) \(\mathstrut +\mathstrut 252707930425928448q^{63} \) \(\mathstrut +\mathstrut 871240582515658816q^{64} \) \(\mathstrut -\mathstrut 196177427386718750q^{65} \) \(\mathstrut -\mathstrut 39391245764988352q^{66} \) \(\mathstrut -\mathstrut 1139262103272878516q^{67} \) \(\mathstrut +\mathstrut 1895976173674409992q^{68} \) \(\mathstrut +\mathstrut 919752424489453968q^{69} \) \(\mathstrut -\mathstrut 565390792218750000q^{70} \) \(\mathstrut -\mathstrut 31406865179074376q^{71} \) \(\mathstrut -\mathstrut 5279093293186620600q^{72} \) \(\mathstrut +\mathstrut 1187325331007472918q^{73} \) \(\mathstrut +\mathstrut 4183638949542864052q^{74} \) \(\mathstrut -\mathstrut 268447875976562500q^{75} \) \(\mathstrut +\mathstrut 1094045334944459120q^{76} \) \(\mathstrut -\mathstrut 4179052633262859552q^{77} \) \(\mathstrut +\mathstrut 214469126119717456q^{78} \) \(\mathstrut +\mathstrut 3296993076150397360q^{79} \) \(\mathstrut -\mathstrut 3954343479718750000q^{80} \) \(\mathstrut +\mathstrut 4134530719458602767q^{81} \) \(\mathstrut -\mathstrut 8794929960295491812q^{82} \) \(\mathstrut -\mathstrut 2397467032735132212q^{83} \) \(\mathstrut +\mathstrut 14109209411744902272q^{84} \) \(\mathstrut -\mathstrut 1487843397160156250q^{85} \) \(\mathstrut +\mathstrut 3513752301252433304q^{86} \) \(\mathstrut -\mathstrut 5768159345858335000q^{87} \) \(\mathstrut +\mathstrut 5515915220105340000q^{88} \) \(\mathstrut -\mathstrut 3350729711921333370q^{89} \) \(\mathstrut -\mathstrut 3089066770316406250q^{90} \) \(\mathstrut -\mathstrut 87629557907868256q^{91} \) \(\mathstrut -\mathstrut 1782877520931221616q^{92} \) \(\mathstrut +\mathstrut 16229414747824917216q^{93} \) \(\mathstrut -\mathstrut 3452936595977488q^{94} \) \(\mathstrut -\mathstrut 1359682874960937500q^{95} \) \(\mathstrut -\mathstrut 36403685930045575936q^{96} \) \(\mathstrut +\mathstrut 3057649965684279854q^{97} \) \(\mathstrut +\mathstrut 17234013451261239982q^{98} \) \(\mathstrut -\mathstrut 23350819231982564212q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(5))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
5.20.a.a \(3\) \(11.441\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1006\) \(-73452\) \(5859375\) \(-54910456\) \(-\) \(q+(-335+\beta _{1})q^{2}+(-24478+18\beta _{1}+\cdots)q^{3}+\cdots\)
5.20.a.b \(4\) \(11.441\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-420\) \(3080\) \(-7812500\) \(214021400\) \(+\) \(q+(-105-\beta _{1})q^{2}+(770+14\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)