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Properties

Label 6.27.b
Level $6$
Weight $27$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $27$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 27 \)
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: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(6, [\chi])\).

Total New Old
Modular forms 28 8 20
Cusp forms 24 8 16
Eisenstein series 4 0 4

Trace form

\( 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9} + O(q^{10}) \) \( 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9} + 18696278507520 q^{10} - 73649293885440 q^{12} + 512429022548560 q^{13} - 1064426665559040 q^{15} + 9007199254740992 q^{16} - 1881283573186560 q^{18} + 13250502825732304 q^{19} - 376087240418977584 q^{21} + 428662713355468800 q^{22} - 301281579173412864 q^{24} - 5623831579932691000 q^{25} + 11144542948278241320 q^{27} - 6147549891468984320 q^{28} - 12961438025281044480 q^{30} - 31284409294003569776 q^{31} - 27135100230528798720 q^{33} - 98764413849435635712 q^{34} + 162870907842406121472 q^{36} - 884494012218278308400 q^{37} + 1550610890749922311440 q^{39} - 627343005833641328640 q^{40} + 2912220856097001308160 q^{42} - 5161357724259210085040 q^{43} + 20490779480380306513920 q^{45} - 10789778429003593678848 q^{46} + 2471260223527012270080 q^{48} - 29984991896355791854440 q^{49} + 55593505357359326429184 q^{51} - 17194264791932123217920 q^{52} + 6309825934293776793600 q^{54} - 76225105088113564293120 q^{55} + 66535314651975639764880 q^{57} - 142582792844514288599040 q^{58} + 35716232168487549665280 q^{60} + 235221054408754640644432 q^{61} - 635461358798759743298160 q^{63} - 302231454903657293676544 q^{64} - 1507842687345202066489344 q^{66} + 4218736573110688595120080 q^{67} - 2608639506957020943089664 q^{69} + 1864568339879729269309440 q^{70} + 63125401729205450833920 q^{72} + 1648536069669962768198800 q^{73} + 2584159434345978668025000 q^{75} - 444613096031842444771328 q^{76} - 313072373593422745436160 q^{78} - 9378866636279258011040624 q^{79} - 746539638785265647226744 q^{81} - 6997685112389596533227520 q^{82} + 12619393734706234851852288 q^{84} - 41457721476781794937282560 q^{85} + 55271553720839002987729920 q^{87} - 14383533866221569677721600 q^{88} + 32441993904208401898536960 q^{90} - 71633324581325574226388320 q^{91} + 18549099857564620426167120 q^{93} + 67962530415252490428088320 q^{94} + 10109332261226898153013248 q^{96} - 92292347027073928712964080 q^{97} + 4908019641378975318951936 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{27}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.27.b.a 6.b 3.b $8$ $25.698$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2194920\) \(0\) \(183211263760\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(274365-33\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{27}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{27}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{27}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)