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Properties

Label 7.17.d
Level $7$
Weight $17$
Character orbit 7.d
Rep. character $\chi_{7}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 17 \)
Character orbit: \([\chi]\) \(=\) 7.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

Trace form

\( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9} + O(q^{10}) \) \( 20 q + 92 q^{2} + 6558 q^{3} - 285924 q^{4} + 241890 q^{5} - 1847944 q^{7} + 23873872 q^{8} + 146092512 q^{9} - 567579804 q^{10} + 487037030 q^{11} - 2240722092 q^{12} + 598121216 q^{14} - 2098975212 q^{15} - 13522996616 q^{16} + 16479299850 q^{17} - 21631627512 q^{18} - 29753076894 q^{19} + 30310552398 q^{21} + 143879888720 q^{22} - 199076938822 q^{23} + 613456300512 q^{24} + 212723266388 q^{25} - 1359419612544 q^{26} + 2531834927748 q^{28} + 438309600272 q^{29} - 2296351012392 q^{30} + 1037434908306 q^{31} - 3523947158064 q^{32} + 411779151054 q^{33} - 7248579242478 q^{35} - 2493315404256 q^{36} + 5318067734218 q^{37} - 9079217417208 q^{38} + 13250117821332 q^{39} + 15010293809208 q^{40} + 16256122433712 q^{42} - 621187489400 q^{43} + 25172272315980 q^{44} - 85040191344096 q^{45} - 15614039192704 q^{46} + 106960600327866 q^{47} - 52978127838580 q^{49} + 35872835226128 q^{50} + 4235281588962 q^{51} + 126484190926632 q^{52} + 29048763888218 q^{53} - 635343594055560 q^{54} + 230352840277168 q^{56} + 366396034764636 q^{57} - 279762037805080 q^{58} - 99092116656282 q^{59} - 173605217618196 q^{60} - 904353032308434 q^{61} + 1188663557133192 q^{63} + 2502182430870944 q^{64} - 500211967540404 q^{65} - 951679982792988 q^{66} - 33326890567694 q^{67} - 964537664673492 q^{68} - 569178593140080 q^{70} + 3111156268483352 q^{71} + 936737429904432 q^{72} - 1146801010325370 q^{73} - 2161044304782140 q^{74} - 4935640048894356 q^{75} + 1321278185203718 q^{77} + 13747974994685232 q^{78} + 126874036566250 q^{79} - 18764997660746184 q^{80} - 2081051947014102 q^{81} - 11916006908925168 q^{82} + 17065299612720828 q^{84} + 27928718307758508 q^{85} - 7493915124549152 q^{86} - 4167264363403248 q^{87} - 10398917942882000 q^{88} - 34000447101257730 q^{89} + 6895892767523928 q^{91} + 113018032389709752 q^{92} - 15597881218045122 q^{93} - 7183919979926376 q^{94} - 19569222088313322 q^{95} - 137281944028491360 q^{96} + 65453414234371436 q^{98} + 142672614742345392 q^{99} + O(q^{100}) \)

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.d.a 7.d 7.d $20$ $11.363$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(92\) \(6558\) \(241890\) \(-1847944\) $\mathrm{SU}(2)[C_{6}]$ \(q+(9-\beta _{1}+9\beta _{2}-\beta _{3})q^{2}+(438+\beta _{1}+\cdots)q^{3}+\cdots\)