Properties

Label 15.10.b
Level $15$
Weight $10$
Character orbit 15.b
Rep. character $\chi_{15}(4,\cdot)$
Character field $\Q$
Dimension $8$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 20 8 12
Cusp forms 16 8 8
Eisenstein series 4 0 4

Trace form

\( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9} + O(q^{10}) \) \( 8 q - 1194 q^{4} - 690 q^{5} + 486 q^{6} - 52488 q^{9} + 67090 q^{10} - 71988 q^{11} + 416364 q^{14} + 80190 q^{15} - 1505630 q^{16} + 851584 q^{19} + 2078100 q^{20} - 1593108 q^{21} + 1242702 q^{24} + 1695500 q^{25} - 877524 q^{26} - 73572 q^{29} + 3086100 q^{30} + 474088 q^{31} - 8124388 q^{34} - 36357180 q^{35} + 7833834 q^{36} + 12959676 q^{39} - 15313390 q^{40} + 93320088 q^{41} - 74555892 q^{44} + 4527090 q^{45} - 9664072 q^{46} + 51329600 q^{49} + 67798200 q^{50} - 108196236 q^{51} - 3188646 q^{54} + 64428480 q^{55} - 67781220 q^{56} + 236526036 q^{59} + 63172710 q^{60} - 357427760 q^{61} - 12137026 q^{64} + 19848300 q^{65} + 23317308 q^{66} + 167059584 q^{69} + 200900520 q^{70} - 156890664 q^{71} - 1523381796 q^{74} - 528573600 q^{75} + 1098697344 q^{76} + 863922280 q^{79} + 630213180 q^{80} + 344373768 q^{81} + 529023636 q^{84} - 2223350420 q^{85} + 997642392 q^{86} + 357382224 q^{89} - 440177490 q^{90} + 214754328 q^{91} - 721679824 q^{94} + 1698584640 q^{95} - 475022718 q^{96} + 472313268 q^{99} + O(q^{100}) \)

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.b.a 15.b 5.b $8$ $7.726$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-690\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(15, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)