Properties

Label 5.20.a
Level $5$
Weight $20$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.20.a.a 5.a 1.a $3$ $11.441$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1006\) \(-73452\) \(5859375\) \(-54910456\) $-$ $\mathrm{SU}(2)$ \(q+(-335+\beta _{1})q^{2}+(-24478+18\beta _{1}+\cdots)q^{3}+\cdots\)
5.20.a.b 5.a 1.a $4$ $11.441$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-420\) \(3080\) \(-7812500\) \(214021400\) $+$ $\mathrm{SU}(2)$ \(q+(-105-\beta _{1})q^{2}+(770+14\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)

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

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