Properties

Label 273.12.a
Level $273$
Weight $12$
Character orbit 273.a
Rep. character $\chi_{273}(1,\cdot)$
Character field $\Q$
Dimension $132$
Newform subspaces $8$
Sturm bound $448$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(448\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(273))\).

Total New Old
Modular forms 416 132 284
Cusp forms 408 132 276
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(17\)
\(-\)\(+\)\(+\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(13\)
Plus space\(+\)\(68\)
Minus space\(-\)\(64\)

Trace form

\( 132q + 92q^{2} + 149244q^{4} - 44712q^{6} - 67228q^{7} - 36156q^{8} + 7794468q^{9} + O(q^{10}) \) \( 132q + 92q^{2} + 149244q^{4} - 44712q^{6} - 67228q^{7} - 36156q^{8} + 7794468q^{9} + 1216688q^{10} - 1081688q^{11} - 468504q^{12} - 4504276q^{14} - 6075000q^{15} + 150496276q^{16} - 2648456q^{17} + 5432508q^{18} - 6760008q^{19} - 16336404q^{21} + 66703056q^{22} - 55563116q^{23} - 248017464q^{24} + 1344850104q^{25} - 128876076q^{28} + 87758708q^{29} - 101848104q^{30} + 414181848q^{31} + 223571684q^{32} + 315373176q^{33} - 815770576q^{34} - 202557964q^{35} + 8812708956q^{36} - 742603824q^{37} - 2508626520q^{38} - 721793592q^{39} + 6922776136q^{40} + 1224527016q^{41} - 530005412q^{43} + 1757509528q^{44} + 1121858960q^{46} + 3519254832q^{47} - 959496192q^{48} + 37286732868q^{49} - 51352724q^{50} - 1011507912q^{51} - 6864464984q^{52} - 3949102268q^{53} - 2640198888q^{54} - 13202342848q^{55} - 19661164740q^{56} + 7138500192q^{57} - 29304997408q^{58} - 2641087176q^{59} - 3626775000q^{60} + 21025134064q^{61} - 38867698168q^{62} - 3969746172q^{63} + 149798650748q^{64} + 4935226556q^{65} - 12971400264q^{66} - 10630979584q^{67} + 43961659280q^{68} + 37649815416q^{69} - 11169528832q^{70} - 27467581344q^{71} - 2134975644q^{72} - 707925000q^{73} + 53360029160q^{74} - 1583609616q^{75} + 105813978256q^{76} + 53333048048q^{77} - 11548697472q^{78} - 30125108788q^{79} + 23041308104q^{80} + 460255540932q^{81} - 95973605616q^{82} - 157889330096q^{83} - 50185433088q^{84} - 325852146760q^{85} + 531116280496q^{86} + 48500492472q^{87} + 86644769712q^{88} + 164505999680q^{89} + 71844209712q^{90} - 49922571608q^{91} + 108534178672q^{92} - 27896920992q^{93} + 729004211496q^{94} + 166065914644q^{95} - 460576612944q^{96} + 149775610296q^{97} + 25987722908q^{98} - 63872594712q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(273))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 13
273.12.a.a \(13\) \(209.758\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-109\) \(3159\) \(-6095\) \(218491\) \(-\) \(-\) \(-\) \(q+(-8-\beta _{1})q^{2}+3^{5}q^{3}+(567+20\beta _{1}+\cdots)q^{4}+\cdots\)
273.12.a.b \(15\) \(209.758\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(100\) \(-3645\) \(6095\) \(-252105\) \(+\) \(+\) \(+\) \(q+(7-\beta _{1})q^{2}-3^{5}q^{3}+(1174-10\beta _{1}+\cdots)q^{4}+\cdots\)
273.12.a.c \(16\) \(209.758\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-63\) \(-3888\) \(-3168\) \(268912\) \(+\) \(-\) \(+\) \(q+(-4+\beta _{1})q^{2}-3^{5}q^{3}+(1298-4\beta _{1}+\cdots)q^{4}+\cdots\)
273.12.a.d \(17\) \(209.758\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-10\) \(4131\) \(-6405\) \(-285719\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+3^{5}q^{3}+(1246-\beta _{1}+\cdots)q^{4}+\cdots\)
273.12.a.e \(17\) \(209.758\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(65\) \(-4131\) \(6405\) \(285719\) \(+\) \(-\) \(-\) \(q+(4-\beta _{1})q^{2}-3^{5}q^{3}+(1071-4\beta _{1}+\cdots)q^{4}+\cdots\)
273.12.a.f \(18\) \(209.758\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(19\) \(4374\) \(-3168\) \(302526\) \(-\) \(-\) \(+\) \(q+(1+\beta _{1})q^{2}+3^{5}q^{3}+(1354-\beta _{1}+\cdots)q^{4}+\cdots\)
273.12.a.g \(18\) \(209.758\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(36\) \(-4374\) \(3168\) \(-302526\) \(+\) \(+\) \(-\) \(q+(2-\beta _{1})q^{2}-3^{5}q^{3}+(1060-3\beta _{1}+\cdots)q^{4}+\cdots\)
273.12.a.h \(18\) \(209.758\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(54\) \(4374\) \(3168\) \(-302526\) \(-\) \(+\) \(-\) \(q+(3-\beta _{1})q^{2}+3^{5}q^{3}+(1147-2\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(273))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(273)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)