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Properties

Label 15.9.f
Level $15$
Weight $9$
Character orbit 15.f
Rep. character $\chi_{15}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 15.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(15, [\chi])\).

Total New Old
Modular forms 36 16 20
Cusp forms 28 16 12
Eisenstein series 8 0 8

Trace form

\( 16 q - 444 q^{5} - 2268 q^{6} + 4540 q^{7} + 17460 q^{8} + O(q^{10}) \) \( 16 q - 444 q^{5} - 2268 q^{6} + 4540 q^{7} + 17460 q^{8} - 25496 q^{10} - 23616 q^{11} + 22680 q^{12} + 133420 q^{13} - 59616 q^{15} - 471380 q^{16} + 573300 q^{17} - 863436 q^{20} + 163944 q^{21} - 234700 q^{22} + 651480 q^{23} + 1459756 q^{25} - 448848 q^{26} - 3567940 q^{28} + 3464856 q^{30} + 1311776 q^{31} + 641460 q^{32} - 3815100 q^{33} + 841080 q^{35} + 5519988 q^{36} - 3607340 q^{37} + 8139840 q^{38} - 324552 q^{40} - 14740104 q^{41} - 9643860 q^{42} - 4805480 q^{43} + 2204496 q^{45} + 14024216 q^{46} + 26529600 q^{47} + 3661200 q^{48} - 38452896 q^{50} - 6168312 q^{51} - 15861080 q^{52} + 16612140 q^{53} - 7043284 q^{55} + 10752000 q^{56} + 4714200 q^{57} + 63562980 q^{58} - 38705364 q^{60} - 12550600 q^{61} - 35190840 q^{62} + 9928980 q^{63} + 125689188 q^{65} + 46958616 q^{66} + 46836760 q^{67} - 197811840 q^{68} + 754260 q^{70} - 85681968 q^{71} - 38185020 q^{72} - 50835800 q^{73} - 51345576 q^{75} + 101166648 q^{76} + 97175880 q^{77} + 131709240 q^{78} + 339741204 q^{80} - 76527504 q^{81} - 181542400 q^{82} - 208234800 q^{83} - 209242748 q^{85} - 187512576 q^{86} - 74298060 q^{87} + 138207420 q^{88} - 76256316 q^{90} + 38623856 q^{91} + 652331400 q^{92} + 159787080 q^{93} - 74686896 q^{95} + 531512604 q^{96} - 138370520 q^{97} - 50186520 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.9.f.a 15.f 5.c $16$ $6.111$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-444\) \(4540\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(15, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)