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Properties

Label 47.20
Level 47
Weight 20
Dimension 1723
Nonzero newspaces 2
Sturm bound 3680
Trace bound 1

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Defining parameters

Level: \( N \) = \( 47 \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 2 \)
Sturm bound: \(3680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(47))\).

Total New Old
Modular forms 1771 1767 4
Cusp forms 1725 1723 2
Eisenstein series 46 44 2

Trace form

\( 1723 q - 935 q^{2} - 101327 q^{3} + 632681 q^{4} + 4754797 q^{5} - 46194647 q^{6} + 33835065 q^{7} + 766663657 q^{8} - 2806727297 q^{9} + O(q^{10}) \) \( 1723 q - 935 q^{2} - 101327 q^{3} + 632681 q^{4} + 4754797 q^{5} - 46194647 q^{6} + 33835065 q^{7} + 766663657 q^{8} - 2806727297 q^{9} + 2168197897 q^{10} + 32424193 q^{11} + 32047722985 q^{12} - 100843230147 q^{13} + 15428800105 q^{14} + 240841142617 q^{15} + 17879523305 q^{16} - 450140199035 q^{17} - 1279867636967 q^{18} + 3420557145297 q^{19} - 1504196816663 q^{20} + 1713814877353 q^{21} + 14785442473 q^{22} - 28073069577767 q^{23} + 38833048719337 q^{24} + 26842816040027 q^{25} - 45984512936567 q^{26} - 24424614229703 q^{27} - 10703797758999 q^{28} - 2275670539043 q^{29} + 109823561043817 q^{30} + 209253760283433 q^{31} - 393799504822295 q^{32} + 1642351388809 q^{33} - 205263930749495 q^{34} - 3889135892689506 q^{35} + 17642919370894697 q^{36} - 4074672445017754 q^{37} + 8152688983544105 q^{38} + 164675253624928 q^{39} - 42891004074375191 q^{40} + 12285866523846712 q^{41} + 56742973392026089 q^{42} - 6073945478757178 q^{43} - 55507653560343063 q^{44} + 19997982881213802 q^{45} + 72040175238101842 q^{46} + 5937678739663763 q^{47} - 289929646181679150 q^{48} - 21652811207587783 q^{49} + 138003121299350265 q^{50} + 227002213283526018 q^{51} - 50767079004601111 q^{52} - 145996944991300698 q^{53} - 49226117225008535 q^{54} + 393360837937995808 q^{55} + 220369260662857705 q^{56} - 453505588952762900 q^{57} - 23343722255196535 q^{58} + 238315055823359430 q^{59} - 1918824343586235415 q^{60} + 714164472615692486 q^{61} + 95419714689255913 q^{62} + 47482932153895033 q^{63} - 188946593725546519 q^{64} + 239745703729098817 q^{65} + 748912233307369 q^{66} + 410205048514764465 q^{67} + 142402752237844201 q^{68} - 1421957120251889111 q^{69} - 36680583712308503 q^{70} + 355804683900835513 q^{71} + 1075907930320604137 q^{72} - 599707550077320267 q^{73} + 154485802561981705 q^{74} + 1359642318060612577 q^{75} + 14642356104921433763 q^{76} - 10458834250397769025 q^{77} + 23107565685283004443 q^{78} - 687730702206441155 q^{79} - 30516158922704280912 q^{80} + 9500015418530994913 q^{81} + 46108202194940442232 q^{82} - 1979578379413200349 q^{83} - 63023151466247094491 q^{84} - 28403907049022925879 q^{85} + 23525689238233995137 q^{86} + 27576471910566770221 q^{87} + 36366432579285571285 q^{88} - 28797292417074914415 q^{89} - 140221837530144297095 q^{90} - 39065928187741454637 q^{91} + 62508450780711452670 q^{92} + 58476941100818444222 q^{93} + 86575684815727565965 q^{94} - 51590692873308200982 q^{95} - 208647569821282394955 q^{96} - 51297700255492356671 q^{97} + 34734808995219780952 q^{98} + 197118797638764574939 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(47))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
47.20.a \(\chi_{47}(1, \cdot)\) 47.20.a.a 34 1
47.20.a.b 39
47.20.c \(\chi_{47}(2, \cdot)\) n/a 1650 22

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(47))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(47)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)