Properties

Label 15.9.c
Level $15$
Weight $9$
Character orbit 15.c
Rep. character $\chi_{15}(11,\cdot)$
Character field $\Q$
Dimension $10$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
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 18 10 8
Cusp forms 14 10 4
Eisenstein series 4 0 4

Trace form

\( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} + O(q^{10}) \) \( 10 q - 112 q^{3} - 786 q^{4} - 5282 q^{6} + 7156 q^{7} + 3922 q^{9} - 8750 q^{10} - 3812 q^{12} - 55464 q^{13} - 21250 q^{15} + 280386 q^{16} - 419800 q^{18} - 231516 q^{19} + 289572 q^{21} + 1129940 q^{22} + 1136334 q^{24} - 781250 q^{25} - 335512 q^{27} - 3340724 q^{28} - 965000 q^{30} + 881620 q^{31} + 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} + 4672616 q^{37} + 1826792 q^{39} + 2913750 q^{40} - 5392860 q^{42} + 7731336 q^{43} - 2142500 q^{45} - 25424604 q^{46} + 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} + 21064016 q^{52} - 7979798 q^{54} - 4377500 q^{55} - 2856304 q^{57} - 4351100 q^{58} + 23016250 q^{60} + 22417020 q^{61} + 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} - 46646024 q^{67} + 33562632 q^{69} - 62992500 q^{70} + 54175560 q^{72} - 129964884 q^{73} + 8750000 q^{75} + 198922436 q^{76} + 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} + 202877560 q^{82} - 197346768 q^{84} - 110682500 q^{85} - 168322540 q^{87} - 484775700 q^{88} + 171878750 q^{90} + 444288464 q^{91} + 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} - 258825724 q^{97} - 33965200 q^{99} + O(q^{100}) \)

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.c.a 15.c 3.b $10$ $6.111$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-112\) \(0\) \(7156\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots\)

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

\( S_{9}^{\mathrm{old}}(15, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)