Properties

Label 10.8.b
Level $10$
Weight $8$
Character orbit 10.b
Rep. character $\chi_{10}(9,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 10.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(10, [\chi])\).

Total New Old
Modular forms 12 4 8
Cusp forms 8 4 4
Eisenstein series 4 0 4

Trace form

\( 4 q - 256 q^{4} + 60 q^{5} + 896 q^{6} - 6788 q^{9} + O(q^{10}) \) \( 4 q - 256 q^{4} + 60 q^{5} + 896 q^{6} - 6788 q^{9} - 640 q^{10} + 17808 q^{11} - 6528 q^{14} - 34960 q^{15} + 16384 q^{16} + 63600 q^{19} - 3840 q^{20} - 63952 q^{21} - 57344 q^{24} + 86100 q^{25} - 56064 q^{26} + 169560 q^{29} + 410240 q^{30} - 394112 q^{31} - 698368 q^{34} - 276720 q^{35} + 434432 q^{36} + 1163424 q^{39} + 40960 q^{40} + 232488 q^{41} - 1139712 q^{44} - 2879420 q^{45} + 1146496 q^{46} + 2520108 q^{49} + 2361600 q^{50} + 361088 q^{51} - 5116160 q^{54} - 526480 q^{55} + 417792 q^{56} + 2093520 q^{59} + 2237440 q^{60} - 5251432 q^{61} - 1048576 q^{64} + 2761440 q^{65} + 2401792 q^{66} + 6514864 q^{69} + 2679680 q^{70} - 7832352 q^{71} - 3126528 q^{74} - 7397600 q^{75} - 4070400 q^{76} + 7727040 q^{79} + 245760 q^{80} + 16428404 q^{81} + 4092928 q^{84} - 7995520 q^{85} + 4411776 q^{86} - 33470040 q^{89} - 15579520 q^{90} + 5340768 q^{91} + 15540352 q^{94} + 31904400 q^{95} + 3670016 q^{96} - 19109776 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.8.b.a 10.b 5.b $4$ $3.124$ \(\Q(i, \sqrt{31})\) None \(0\) \(0\) \(60\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(3\beta _{1}-\beta _{3})q^{3}-2^{6}q^{4}+(15+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)