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Properties

Label 6.21.b
Level $6$
Weight $21$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 21 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(6, [\chi])\).

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

Trace form

\( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9} + O(q^{10}) \) \( 6 q + 18846 q^{3} - 3145728 q^{4} + 35057664 q^{6} - 566671812 q^{7} + 1944941382 q^{9} + 5360984064 q^{10} - 9880731648 q^{12} - 49898545620 q^{13} + 487708151328 q^{15} + 1649267441664 q^{16} - 3239129751552 q^{18} + 15927597287292 q^{19} - 20677554127188 q^{21} + 21184189636608 q^{22} - 18380312543232 q^{24} + 337510512308454 q^{25} - 1019514529044162 q^{27} + 297099230969856 q^{28} - 920809286295552 q^{30} + 1832545426397628 q^{31} - 3503562514347744 q^{33} + 2508713101983744 q^{34} - 1019709427286016 q^{36} + 424332326872812 q^{37} + 13854943345637340 q^{39} - 2810699612946432 q^{40} + 30169507188989952 q^{42} - 49488752333951556 q^{43} + 64297936569436992 q^{45} - 51218624034717696 q^{46} + 5180349034266624 q^{48} - 185965132589503470 q^{49} + 114461935953291648 q^{51} + 26161208686018560 q^{52} - 103567464750919680 q^{54} + 468503586680075712 q^{55} - 1250127589109383188 q^{57} + 330130684975472640 q^{58} - 255699531243454464 q^{60} + 3301830012872093484 q^{61} - 724019288731292484 q^{63} - 864691128455135232 q^{64} + 1110947414199017472 q^{66} - 2779226272508556228 q^{67} + 667934407322175168 q^{69} - 1866219302039371776 q^{70} + 1698236859181694976 q^{72} - 9149401536792501300 q^{73} + 9127347583517050878 q^{75} - 8350648126559748096 q^{76} + 19815256334884331520 q^{78} + 90056048403257148 q^{79} - 13310358127786728378 q^{81} - 19709381871486517248 q^{82} + 10840993498235142144 q^{84} + 78223886062534003968 q^{85} - 87334395308747540640 q^{87} - 11106616416197935104 q^{88} + 60406983770669457408 q^{90} + 132462766690215009720 q^{91} - 157075923546140581332 q^{93} - 106728395801434030080 q^{94} + 9636577302666018816 q^{96} + 92028905119987573836 q^{97} - 224342570810992842432 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{21}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.21.b.a 6.b 3.b $6$ $15.211$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(18846\) \(0\) \(-566671812\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(3141-11\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{21}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{21}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{21}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)