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Properties

Label 36.27.d
Level $36$
Weight $27$
Character orbit 36.d
Rep. character $\chi_{36}(19,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $5$
Sturm bound $162$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 27 \)
Character orbit: \([\chi]\) \(=\) 36.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(162\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(36, [\chi])\).

Total New Old
Modular forms 160 66 94
Cusp forms 152 64 88
Eisenstein series 8 2 6

Trace form

\( 64 q + 182 q^{2} + 16622548 q^{4} - 298775876 q^{5} - 80878469776 q^{8} + O(q^{10}) \) \( 64 q + 182 q^{2} + 16622548 q^{4} - 298775876 q^{5} - 80878469776 q^{8} + 17896797229052 q^{10} - 360422806802776 q^{13} - 1272082528618248 q^{14} - 10562033382653168 q^{16} - 6118189913625500 q^{17} - 196888688274264488 q^{20} - 99533843311304616 q^{22} + 15237151833172813656 q^{25} + 4866861056527938316 q^{26} + 7202447501908552368 q^{28} - 14562292864659592340 q^{29} - 141230330271386553568 q^{32} + 6553013275635700868 q^{34} - 299427843344904912448 q^{37} - 143683386929103948552 q^{38} - 533411768193326392480 q^{40} + 1404923820046466875588 q^{41} + 6762096325328859151536 q^{44} - 6353008345347541932576 q^{46} - 84521955471649330650272 q^{49} + 8015945731473509572818 q^{50} - 46466012845571411395768 q^{52} - 34655558409075751996532 q^{53} - 99916163946883151481600 q^{56} + 122843279749334556621932 q^{58} + 3822911076424529318624 q^{61} + 220308284714856606194376 q^{62} + 379379052023371843670272 q^{64} + 843596426170529314835768 q^{65} + 1620862611915601882556680 q^{68} + 1354336211379729039672048 q^{70} - 1119368965791412799624872 q^{73} + 1109773792368892869363772 q^{74} + 5708143030895865704513520 q^{76} + 6344577546738544398015264 q^{77} - 19198282177879730223459872 q^{80} - 8978762342871932762252956 q^{82} - 35872977683228574154111256 q^{85} - 12014769422345293985760408 q^{86} + 12872342127705106755836160 q^{88} - 59204822557518149174600492 q^{89} + 24583251190748285918614848 q^{92} - 22168796938107923890723920 q^{94} + 16092655175585267506088984 q^{97} - 21480958365499067070173578 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{27}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.27.d.a 36.d 4.b $1$ $154.185$ \(\Q\) \(\Q(\sqrt{-1}) \) \(-8192\) \(0\) \(-1195103512\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{13}q^{2}+2^{26}q^{4}-1195103512q^{5}+\cdots\)
36.27.d.b 36.d 4.b $1$ $154.185$ \(\Q\) \(\Q(\sqrt{-1}) \) \(8192\) \(0\) \(1195103512\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{13}q^{2}+2^{26}q^{4}+1195103512q^{5}+\cdots\)
36.27.d.c 36.d 4.b $12$ $154.185$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-180\) \(0\) \(298775880\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-15+\beta _{1})q^{2}+(-1879252-15\beta _{1}+\cdots)q^{4}+\cdots\)
36.27.d.d 36.d 4.b $24$ $154.185$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
36.27.d.e 36.d 4.b $26$ $154.185$ None \(362\) \(0\) \(-597551756\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{27}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{27}^{\mathrm{old}}(36, [\chi]) \simeq \) \(S_{27}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)