Properties

Label 7.10.a
Level $7$
Weight $10$
Character orbit 7.a
Rep. character $\chi_{7}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $6$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(7))\).

Total New Old
Modular forms 7 5 2
Cusp forms 5 5 0
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.
\(+\)\(2\)
\(-\)\(3\)

Trace form

\( 5 q + 15 q^{2} - 2 q^{3} + 937 q^{4} - 684 q^{5} + 926 q^{6} + 2401 q^{7} + 16671 q^{8} - 14963 q^{9} + O(q^{10}) \) \( 5 q + 15 q^{2} - 2 q^{3} + 937 q^{4} - 684 q^{5} + 926 q^{6} + 2401 q^{7} + 16671 q^{8} - 14963 q^{9} - 54476 q^{10} + 31872 q^{11} - 54250 q^{12} - 46312 q^{13} + 64827 q^{14} - 106832 q^{15} + 482209 q^{16} + 552774 q^{17} + 58775 q^{18} - 702574 q^{19} - 1448328 q^{20} + 408170 q^{21} - 1669160 q^{22} + 2663760 q^{23} + 1851666 q^{24} + 5154943 q^{25} - 12912480 q^{26} - 2246732 q^{27} + 5226977 q^{28} - 5921766 q^{29} + 12149072 q^{30} + 5336700 q^{31} + 26506527 q^{32} - 35900576 q^{33} - 6228318 q^{34} + 9104592 q^{35} - 41009095 q^{36} + 32131170 q^{37} + 46984530 q^{38} + 38427256 q^{39} - 115269264 q^{40} - 33524106 q^{41} + 21373702 q^{42} - 57566072 q^{43} + 78361008 q^{44} + 52112980 q^{45} + 102115248 q^{46} - 92563980 q^{47} - 12007714 q^{48} + 28824005 q^{49} - 14987571 q^{50} + 33824628 q^{51} - 47441660 q^{52} + 12312798 q^{53} - 65044828 q^{54} - 23377216 q^{55} + 27465039 q^{56} + 40252228 q^{57} - 92605826 q^{58} - 49659318 q^{59} - 103385632 q^{60} + 236063228 q^{61} + 7926732 q^{62} - 88930639 q^{63} + 155269313 q^{64} - 5696040 q^{65} - 91316416 q^{66} - 497097124 q^{67} + 909131622 q^{68} + 62722704 q^{69} - 339126844 q^{70} + 503008320 q^{71} - 888461985 q^{72} - 154939878 q^{73} - 687124938 q^{74} + 1092259130 q^{75} + 1011351754 q^{76} - 93062760 q^{77} + 375103736 q^{78} - 491877560 q^{79} - 1083429216 q^{80} - 621573311 q^{81} + 952261394 q^{82} - 656493222 q^{83} - 380611322 q^{84} + 611654472 q^{85} - 1297812864 q^{86} - 593687252 q^{87} + 220113984 q^{88} + 1143083874 q^{89} + 2030209892 q^{90} + 16201948 q^{91} + 361692000 q^{92} + 901734552 q^{93} + 1235781636 q^{94} - 1098323088 q^{95} - 1381595390 q^{96} - 2280214314 q^{97} + 86472015 q^{98} - 491561312 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(7))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7
7.10.a.a $2$ $3.605$ \(\Q(\sqrt{193}) \) None \(-6\) \(-86\) \(-2238\) \(-4802\) $+$ \(q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots\)
7.10.a.b $3$ $3.605$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(21\) \(84\) \(1554\) \(7203\) $-$ \(q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots\)