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Properties

Label 7.20.a
Level $7$
Weight $20$
Character orbit 7.a
Rep. character $\chi_{7}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $13$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(13\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(7))\).

Total New Old
Modular forms 13 9 4
Cusp forms 11 9 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.

\(7\)Dim
\(+\)\(5\)
\(-\)\(4\)

Trace form

\( 9 q - 457 q^{2} - 61940 q^{3} + 2365625 q^{4} + 6998986 q^{5} - 33082306 q^{6} - 40353607 q^{7} + 158802903 q^{8} - 320733899 q^{9} + O(q^{10}) \) \( 9 q - 457 q^{2} - 61940 q^{3} + 2365625 q^{4} + 6998986 q^{5} - 33082306 q^{6} - 40353607 q^{7} + 158802903 q^{8} - 320733899 q^{9} + 2020550164 q^{10} + 3711008020 q^{11} + 12443940278 q^{12} - 23169459110 q^{13} - 9160268789 q^{14} + 65539206328 q^{15} + 23617182593 q^{16} + 440055585546 q^{17} + 431797116311 q^{18} + 1788025531804 q^{19} - 363857387992 q^{20} + 116541217016 q^{21} + 4633436545696 q^{22} - 8070758682744 q^{23} + 49030574701314 q^{24} - 3501185602969 q^{25} - 4461838184272 q^{26} - 89465268754664 q^{27} - 48958327681431 q^{28} - 83782413854114 q^{29} + 82423026276272 q^{30} + 611354699342768 q^{31} - 607111178477273 q^{32} - 94956677393696 q^{33} - 551538251872158 q^{34} - 483121695847042 q^{35} - 979932496825711 q^{36} + 1857298429630838 q^{37} + 4355335082498690 q^{38} - 5129488802897480 q^{39} + 898221696698880 q^{40} + 2300257278711602 q^{41} - 63201092918474 q^{42} - 4321769927527020 q^{43} + 4420653527599496 q^{44} + 7619310215799442 q^{45} - 8537176360340544 q^{46} + 2414187236069568 q^{47} + 10342817293230494 q^{48} + 14655722381194041 q^{49} + 16231907133343549 q^{50} - 44307863009050344 q^{51} - 45887599353160572 q^{52} - 4991203473261090 q^{53} - 55703148945073372 q^{54} + 24908981404028552 q^{55} + 26584416239277519 q^{56} + 180393289926857176 q^{57} - 77102105404882058 q^{58} - 148172062576543212 q^{59} + 17424658930550144 q^{60} - 38050475879924654 q^{61} + 31893695109227100 q^{62} - 14118716836748755 q^{63} + 107182776585632529 q^{64} + 237550771498457788 q^{65} - 39028738084596880 q^{66} + 189607239949007740 q^{67} + 419075445605477430 q^{68} - 573452520786479808 q^{69} - 194290414935657628 q^{70} - 497722379105575032 q^{71} + 537977682008903055 q^{72} + 1028054062862983082 q^{73} - 1337093424244967298 q^{74} + 1954433437090178228 q^{75} - 1266879992646953286 q^{76} - 572084856078730708 q^{77} - 2764063643672780680 q^{78} + 562856763571379520 q^{79} - 132445314706230544 q^{80} - 109798326122456807 q^{81} + 4184292137189993234 q^{82} - 1568597418891633060 q^{83} - 716267746129869290 q^{84} + 4467945753445054644 q^{85} - 4583158790771403896 q^{86} - 4663644663267851864 q^{87} - 4458222595514191128 q^{88} + 1457312653336730506 q^{89} + 8498019374937461828 q^{90} - 1007788187053544106 q^{91} + 20364885334224050448 q^{92} - 7128638715269019792 q^{93} - 18121300886354395692 q^{94} - 951731142119380520 q^{95} + 15732725157210348658 q^{96} + 14439796020820494170 q^{97} - 744185014245075193 q^{98} + 27936330282272490628 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(7))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7
7.20.a.a 7.a 1.a $4$ $16.017$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-342\) \(-29526\) \(-2486610\) \(161414428\) $-$ $\mathrm{SU}(2)$ \(q+(-86+\beta _{1})q^{2}+(-7378-8\beta _{1}+\cdots)q^{3}+\cdots\)
7.20.a.b 7.a 1.a $5$ $16.017$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-115\) \(-32414\) \(9485596\) \(-201768035\) $+$ $\mathrm{SU}(2)$ \(q+(-23-\beta _{1})q^{2}+(-6483+4\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(7))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(7)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)