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Properties

Label 7.17.b
Level $7$
Weight $17$
Character orbit 7.b
Rep. character $\chi_{7}(6,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.17.b.a 7.b 7.b $1$ $11.363$ \(\Q\) \(\Q(\sqrt{-7}) \) \(449\) \(0\) \(0\) \(5764801\) $\mathrm{U}(1)[D_{2}]$ \(q+449q^{2}+136065q^{4}+7^{8}q^{7}+31667521q^{8}+\cdots\)
7.17.b.b 7.b 7.b $8$ $11.363$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-544\) \(0\) \(0\) \(-3034472\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-68-\beta _{2})q^{2}+\beta _{1}q^{3}+(2348+139\beta _{2}+\cdots)q^{4}+\cdots\)