Properties

Label 10.14.b
Level $10$
Weight $14$
Character orbit 10.b
Rep. character $\chi_{10}(9,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 14 \)
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: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(10, [\chi])\).

Total New Old
Modular forms 22 6 16
Cusp forms 18 6 12
Eisenstein series 4 0 4

Trace form

\( 6 q - 24576 q^{4} - 2470 q^{5} - 23296 q^{6} + 4260922 q^{9} + O(q^{10}) \) \( 6 q - 24576 q^{4} - 2470 q^{5} - 23296 q^{6} + 4260922 q^{9} - 2269440 q^{10} + 673672 q^{11} - 1211648 q^{14} + 80128760 q^{15} + 100663296 q^{16} + 142606200 q^{19} + 10117120 q^{20} - 926360008 q^{21} + 95420416 q^{24} + 1820907150 q^{25} - 3369156096 q^{26} + 1402368660 q^{29} + 6491083520 q^{30} - 22270466688 q^{31} + 10743816192 q^{34} + 40910703880 q^{35} - 17452736512 q^{36} + 80990077584 q^{39} + 9295626240 q^{40} - 159550828628 q^{41} - 2759360512 q^{44} + 112298555110 q^{45} - 48346742016 q^{46} - 142584010062 q^{49} + 33045516800 q^{50} + 47596879232 q^{51} + 104187005440 q^{54} - 465712133640 q^{55} + 4962910208 q^{56} - 129517581080 q^{59} - 328207400960 q^{60} + 2208324934212 q^{61} - 412316860416 q^{64} - 475107396240 q^{65} + 1429010971648 q^{66} - 2470574584136 q^{69} - 1324581354240 q^{70} + 1016718596592 q^{71} + 1548283182592 q^{74} - 1495698537200 q^{75} - 584114995200 q^{76} - 23303633760 q^{79} - 41439723520 q^{80} - 2585393406754 q^{81} + 3794370592768 q^{84} + 9460560132480 q^{85} - 10908216246016 q^{86} - 1102941191140 q^{89} - 1112244801280 q^{90} - 9640398296208 q^{91} + 20956004804352 q^{94} + 26900168949000 q^{95} - 390842023936 q^{96} - 11776973376136 q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.14.b.a 10.b 5.b $6$ $10.723$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-2470\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}-2^{12}q^{4}+(-412+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{14}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{14}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)