Properties

Label 273.8.a
Level $273$
Weight $8$
Character orbit 273.a
Rep. character $\chi_{273}(1,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $8$
Sturm bound $298$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 273.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(298\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(273))\).

Total New Old
Modular forms 264 84 180
Cusp forms 256 84 172
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.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(44\)
Minus space\(-\)\(40\)

Trace form

\( 84 q + 28 q^{2} + 5116 q^{4} + 216 q^{6} - 1372 q^{7} + 2436 q^{8} + 61236 q^{9} + O(q^{10}) \) \( 84 q + 28 q^{2} + 5116 q^{4} + 216 q^{6} - 1372 q^{7} + 2436 q^{8} + 61236 q^{9} - 16592 q^{10} + 2408 q^{11} + 15336 q^{12} + 17836 q^{14} - 27000 q^{15} + 273556 q^{16} - 26104 q^{17} + 20412 q^{18} + 166520 q^{19} - 37044 q^{21} + 48208 q^{22} - 92380 q^{23} + 109512 q^{24} + 1479184 q^{25} - 215404 q^{28} - 57380 q^{29} - 181224 q^{30} - 729480 q^{31} + 870436 q^{32} + 81864 q^{33} + 400048 q^{34} + 58996 q^{35} + 3729564 q^{36} + 157616 q^{37} - 2969304 q^{38} - 474552 q^{39} - 1675064 q^{40} + 232824 q^{41} + 1432252 q^{43} + 4594520 q^{44} + 1668304 q^{46} - 2327184 q^{47} + 1963008 q^{48} + 9882516 q^{49} + 11959916 q^{50} - 3074760 q^{51} + 17576 q^{52} + 283532 q^{53} + 157464 q^{54} + 5392512 q^{55} + 7651644 q^{56} - 4409856 q^{57} + 3637344 q^{58} - 4218504 q^{59} + 3321000 q^{60} - 2022800 q^{61} + 2567176 q^{62} - 1000188 q^{63} + 14283516 q^{64} - 1783964 q^{65} + 6577848 q^{66} + 3201408 q^{67} - 11479664 q^{68} + 8791848 q^{69} - 6717312 q^{70} + 7291968 q^{71} + 1775844 q^{72} - 10149624 q^{73} + 25193128 q^{74} - 1867536 q^{75} + 38061328 q^{76} - 11914448 q^{77} - 1898208 q^{78} + 12342492 q^{79} - 72639416 q^{80} + 44641044 q^{81} + 1577296 q^{82} + 9294800 q^{83} - 7112448 q^{84} - 3816280 q^{85} - 19754128 q^{86} + 681048 q^{87} + 61296 q^{88} + 3562432 q^{89} - 12095568 q^{90} - 6028568 q^{91} + 81696752 q^{92} + 20021472 q^{93} - 61495192 q^{94} - 23303836 q^{95} - 6393168 q^{96} - 25335256 q^{97} + 3294172 q^{98} + 1755432 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(273))\) 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
273.8.a.a \(7\) \(85.281\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-5\) \(189\) \(-330\) \(2401\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+3^{3}q^{3}+(22+\beta _{4}+\cdots)q^{4}+\cdots\)
273.8.a.b \(9\) \(85.281\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(4\) \(-243\) \(330\) \(-3087\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-3^{3}q^{3}+(40-\beta _{1}+\beta _{3})q^{4}+\cdots\)
273.8.a.c \(10\) \(85.281\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-7\) \(-270\) \(123\) \(3430\) \(+\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}-3^{3}q^{3}+(52+\beta _{2}+\cdots)q^{4}+\cdots\)
273.8.a.d \(11\) \(85.281\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-10\) \(297\) \(-170\) \(-3773\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+3^{3}q^{3}+(69-2\beta _{1}+\cdots)q^{4}+\cdots\)
273.8.a.e \(11\) \(85.281\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(25\) \(-297\) \(170\) \(3773\) \(+\) \(-\) \(-\) \(q+(2+\beta _{1})q^{2}-3^{3}q^{3}+(58+4\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
273.8.a.f \(12\) \(85.281\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-324\) \(-123\) \(-4116\) \(+\) \(+\) \(-\) \(q+(-1-\beta _{1})q^{2}-3^{3}q^{3}+(62+2\beta _{1}+\cdots)q^{4}+\cdots\)
273.8.a.g \(12\) \(85.281\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(324\) \(-123\) \(-4116\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+3^{3}q^{3}+(85+\beta _{2})q^{4}+\cdots\)
273.8.a.h \(12\) \(85.281\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(27\) \(324\) \(123\) \(4116\) \(-\) \(-\) \(+\) \(q+(2+\beta _{1})q^{2}+3^{3}q^{3}+(76+3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(273))\) into lower level spaces

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