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Properties

Label 21.9.b
Level $21$
Weight $9$
Character orbit 21.b
Rep. character $\chi_{21}(8,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 21.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(21, [\chi])\).

Total New Old
Modular forms 24 16 8
Cusp forms 20 16 4
Eisenstein series 4 0 4

Trace form

\( 16 q - 182 q^{3} - 1572 q^{4} - 5026 q^{6} + 9304 q^{9} + O(q^{10}) \) \( 16 q - 182 q^{3} - 1572 q^{4} - 5026 q^{6} + 9304 q^{9} - 7364 q^{10} + 87458 q^{12} - 47460 q^{13} + 115876 q^{15} + 487428 q^{16} - 525832 q^{18} - 377916 q^{19} - 81634 q^{21} + 275824 q^{22} - 281862 q^{24} - 1603704 q^{25} + 1070398 q^{27} - 595448 q^{28} + 1232108 q^{30} + 82936 q^{31} - 1601684 q^{33} + 10074288 q^{34} + 1486844 q^{36} - 10527200 q^{37} - 5636228 q^{39} - 412860 q^{40} + 5642350 q^{42} + 3062000 q^{43} + 4598860 q^{45} - 20247120 q^{46} - 17988082 q^{48} + 13176688 q^{49} + 14676 q^{51} + 36568868 q^{52} + 28779254 q^{54} + 39521384 q^{55} + 26828416 q^{57} - 18337424 q^{58} - 70421188 q^{60} - 55649580 q^{61} + 16240364 q^{63} - 127448396 q^{64} - 14627116 q^{66} + 48398760 q^{67} - 56397936 q^{69} - 32509540 q^{70} + 165877344 q^{72} - 82345928 q^{73} - 24802666 q^{75} + 333954740 q^{76} - 63454948 q^{78} - 1300864 q^{79} + 9523768 q^{81} + 108648344 q^{82} + 41225170 q^{84} - 64318944 q^{85} - 87414236 q^{87} + 172885848 q^{88} - 249384352 q^{90} - 240100 q^{91} + 137670888 q^{93} - 559369440 q^{94} + 504157654 q^{96} - 337523648 q^{97} - 156506576 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
21.9.b.a 21.b 3.b $16$ $8.555$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-182\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-11+\beta _{1}-\beta _{3})q^{3}+(-98+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)