Properties

Label 15.10.e
Level $15$
Weight $10$
Character orbit 15.e
Rep. character $\chi_{15}(2,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 15.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(15, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 32 32 0
Eisenstein series 8 8 0

Trace form

\( 32 q - 150 q^{3} - 4548 q^{6} - 9760 q^{7} + O(q^{10}) \) \( 32 q - 150 q^{3} - 4548 q^{6} - 9760 q^{7} - 39820 q^{10} + 191940 q^{12} + 114260 q^{13} - 40230 q^{15} - 1494724 q^{16} + 994800 q^{18} + 592212 q^{21} + 308260 q^{22} + 5808020 q^{25} + 4786830 q^{27} - 12953300 q^{28} - 17343060 q^{30} + 16124104 q^{31} + 19638120 q^{33} - 48943956 q^{36} - 35578660 q^{37} + 144132840 q^{40} + 46648260 q^{42} - 118721020 q^{43} - 129688380 q^{45} + 3145024 q^{46} + 275395140 q^{48} - 64226868 q^{51} - 157103680 q^{52} + 144539740 q^{55} + 48163500 q^{57} - 209634300 q^{58} - 140815620 q^{60} + 63607744 q^{61} + 89858580 q^{63} + 358931400 q^{66} + 153311540 q^{67} + 420519420 q^{70} - 1534046760 q^{72} + 628070360 q^{73} + 138090210 q^{75} - 2457023472 q^{76} - 403337880 q^{78} + 2250542952 q^{81} + 4138031440 q^{82} + 108907340 q^{85} - 2878139760 q^{87} - 595851300 q^{88} + 693868920 q^{90} - 4369040216 q^{91} - 293672640 q^{93} + 7291125636 q^{96} + 3987642200 q^{97} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.10.e.a 15.e 15.e $32$ $7.726$ None \(0\) \(-150\) \(0\) \(-9760\) $\mathrm{SU}(2)[C_{4}]$