Properties

Label 17.10.c
Level $17$
Weight $10$
Character orbit 17.c
Rep. character $\chi_{17}(4,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(17, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 24 24 0
Eisenstein series 4 4 0

Trace form

\( 24q + 144q^{3} - 5124q^{4} - 1710q^{5} - 8174q^{6} + 3810q^{7} + O(q^{10}) \) \( 24q + 144q^{3} - 5124q^{4} - 1710q^{5} - 8174q^{6} + 3810q^{7} + 21946q^{10} + 18132q^{11} - 95142q^{12} + 244832q^{13} - 341100q^{14} - 279932q^{16} - 98022q^{17} + 888764q^{18} + 1364262q^{20} - 775748q^{21} - 4573190q^{22} - 377526q^{23} - 307054q^{24} + 3996108q^{27} - 1024780q^{28} + 2160042q^{29} + 39084792q^{30} - 585086q^{31} - 30349992q^{33} + 4441318q^{34} - 25532364q^{35} + 1515390q^{37} + 13171392q^{38} - 25687084q^{39} - 63240118q^{40} - 72707928q^{41} - 3606450q^{44} + 156729418q^{45} + 118549536q^{46} + 153365328q^{47} + 26098270q^{48} - 236105676q^{50} + 256903592q^{51} - 209898380q^{52} - 187411976q^{54} + 255767540q^{55} - 107638596q^{56} - 443390988q^{57} - 281433730q^{58} + 52149382q^{61} + 176928228q^{62} + 620111642q^{63} + 1006108924q^{64} - 489714396q^{65} - 26076868q^{67} - 308011950q^{68} - 751973532q^{69} + 149240178q^{71} + 1171736028q^{72} - 175256556q^{73} - 37609818q^{74} - 233543476q^{75} - 1202722924q^{78} - 469987182q^{79} + 481103586q^{80} + 347156560q^{81} - 984422080q^{82} - 935672904q^{84} - 725828294q^{85} + 690159588q^{86} + 992281114q^{88} - 191594460q^{89} + 914946474q^{90} + 926854816q^{91} + 3064830552q^{92} + 1213246572q^{95} + 3594247550q^{96} - 2200567348q^{97} - 4413444720q^{98} - 1224966600q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(17, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.10.c.a \(24\) \(8.756\) None \(0\) \(144\) \(-1710\) \(3810\)