Properties

Label 10.6.b
Level $10$
Weight $6$
Character orbit 10.b
Rep. character $\chi_{10}(9,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(10, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 6 2 4
Eisenstein series 4 0 4

Trace form

\( 2 q - 32 q^{4} + 110 q^{5} - 112 q^{6} + 94 q^{9} + O(q^{10}) \) \( 2 q - 32 q^{4} + 110 q^{5} - 112 q^{6} + 94 q^{9} - 80 q^{10} - 296 q^{11} + 1264 q^{14} - 280 q^{15} + 512 q^{16} - 4440 q^{19} - 1760 q^{20} + 4424 q^{21} + 1792 q^{24} + 5850 q^{25} - 5472 q^{26} + 540 q^{29} - 6160 q^{30} - 4096 q^{31} + 16384 q^{34} + 3160 q^{35} - 1504 q^{36} - 19152 q^{39} + 1280 q^{40} - 4796 q^{41} + 4736 q^{44} + 5170 q^{45} + 9968 q^{46} - 16314 q^{49} - 8800 q^{50} + 57344 q^{51} - 32480 q^{54} - 16280 q^{55} - 20224 q^{56} + 79480 q^{59} + 4480 q^{60} - 84596 q^{61} - 8192 q^{64} - 13680 q^{65} + 16576 q^{66} + 34888 q^{69} + 69520 q^{70} - 8496 q^{71} - 34976 q^{74} - 30800 q^{75} + 71040 q^{76} - 70560 q^{79} + 28160 q^{80} - 90838 q^{81} - 70784 q^{84} + 40960 q^{85} - 18352 q^{86} + 170420 q^{89} - 3760 q^{90} + 216144 q^{91} - 85456 q^{94} - 244200 q^{95} - 28672 q^{96} - 13912 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.6.b.a 10.b 5.b $2$ $1.604$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(110\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)