Properties

Label 7.17.b
Level 7
Weight 17
Character orbit b
Rep. character \(\chi_{7}(6,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 2
Sturm bound 11
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 7.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(11\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(7, [\chi])\).

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

Trace form

\(9q \) \(\mathstrut -\mathstrut 95q^{2} \) \(\mathstrut +\mathstrut 154849q^{4} \) \(\mathstrut +\mathstrut 2730329q^{7} \) \(\mathstrut -\mathstrut 4196287q^{8} \) \(\mathstrut +\mathstrut 1112841q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut -\mathstrut 95q^{2} \) \(\mathstrut +\mathstrut 154849q^{4} \) \(\mathstrut +\mathstrut 2730329q^{7} \) \(\mathstrut -\mathstrut 4196287q^{8} \) \(\mathstrut +\mathstrut 1112841q^{9} \) \(\mathstrut +\mathstrut 174708658q^{11} \) \(\mathstrut +\mathstrut 508161409q^{14} \) \(\mathstrut +\mathstrut 83393280q^{15} \) \(\mathstrut +\mathstrut 944480257q^{16} \) \(\mathstrut +\mathstrut 12095576865q^{18} \) \(\mathstrut +\mathstrut 45847234944q^{21} \) \(\mathstrut -\mathstrut 149080234622q^{22} \) \(\mathstrut -\mathstrut 66418990670q^{23} \) \(\mathstrut +\mathstrut 214554141705q^{25} \) \(\mathstrut +\mathstrut 407601925409q^{28} \) \(\mathstrut -\mathstrut 1011224475950q^{29} \) \(\mathstrut -\mathstrut 192018300480q^{30} \) \(\mathstrut +\mathstrut 1246727659713q^{32} \) \(\mathstrut +\mathstrut 371925382080q^{35} \) \(\mathstrut +\mathstrut 1329492693537q^{36} \) \(\mathstrut +\mathstrut 3013910767570q^{37} \) \(\mathstrut -\mathstrut 7975804007808q^{39} \) \(\mathstrut -\mathstrut 13160568536640q^{42} \) \(\mathstrut +\mathstrut 17886342128050q^{43} \) \(\mathstrut +\mathstrut 10547147011458q^{44} \) \(\mathstrut -\mathstrut 34309179060542q^{46} \) \(\mathstrut +\mathstrut 5782395780105q^{49} \) \(\mathstrut -\mathstrut 28052802777695q^{50} \) \(\mathstrut +\mathstrut 58670380591488q^{51} \) \(\mathstrut +\mathstrut 3276341798098q^{53} \) \(\mathstrut +\mathstrut 167439837594113q^{56} \) \(\mathstrut -\mathstrut 196163055495360q^{57} \) \(\mathstrut +\mathstrut 206882371360258q^{58} \) \(\mathstrut -\mathstrut 335782392744960q^{60} \) \(\mathstrut +\mathstrut 471894830050329q^{63} \) \(\mathstrut -\mathstrut 671014863826303q^{64} \) \(\mathstrut +\mathstrut 573279455461440q^{65} \) \(\mathstrut -\mathstrut 1283371172622030q^{67} \) \(\mathstrut +\mathstrut 1268642086877760q^{70} \) \(\mathstrut +\mathstrut 211393036264498q^{71} \) \(\mathstrut +\mathstrut 2923189657453953q^{72} \) \(\mathstrut -\mathstrut 6634722002957182q^{74} \) \(\mathstrut +\mathstrut 3011626029812050q^{77} \) \(\mathstrut +\mathstrut 192459573633600q^{78} \) \(\mathstrut +\mathstrut 6972603796817970q^{79} \) \(\mathstrut -\mathstrut 12764014742722743q^{81} \) \(\mathstrut +\mathstrut 12924747561148416q^{84} \) \(\mathstrut -\mathstrut 5815379514337920q^{85} \) \(\mathstrut +\mathstrut 17325072331024898q^{86} \) \(\mathstrut -\mathstrut 32762705093517502q^{88} \) \(\mathstrut +\mathstrut 23929798963272384q^{91} \) \(\mathstrut -\mathstrut 20053897682995902q^{92} \) \(\mathstrut +\mathstrut 27012151562451840q^{93} \) \(\mathstrut -\mathstrut 53204702857107840q^{95} \) \(\mathstrut +\mathstrut 58200007193049505q^{98} \) \(\mathstrut -\mathstrut 26745224197428558q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.17.b.a \(1\) \(11.363\) \(\Q\) \(\Q(\sqrt{-7}) \) \(449\) \(0\) \(0\) \(5764801\) \(q+449q^{2}+136065q^{4}+7^{8}q^{7}+31667521q^{8}+\cdots\)
7.17.b.b \(8\) \(11.363\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-544\) \(0\) \(0\) \(-3034472\) \(q+(-68-\beta _{2})q^{2}+\beta _{1}q^{3}+(2348+139\beta _{2}+\cdots)q^{4}+\cdots\)