Properties

Label 273.2.a
Level $273$
Weight $2$
Character orbit 273.a
Rep. character $\chi_{273}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $5$
Sturm bound $74$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(273))\).

Total New Old
Modular forms 40 11 29
Cusp forms 33 11 22
Eisenstein series 7 0 7

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
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(4\)
Minus space\(-\)\(7\)

Trace form

\( 11 q + q^{2} - q^{3} + 17 q^{4} - 6 q^{5} + 5 q^{6} + 3 q^{7} - 3 q^{8} + 11 q^{9} + O(q^{10}) \) \( 11 q + q^{2} - q^{3} + 17 q^{4} - 6 q^{5} + 5 q^{6} + 3 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{10} - 4 q^{11} + q^{12} - q^{13} + q^{14} + 2 q^{15} + 25 q^{16} - 10 q^{17} + q^{18} + 4 q^{19} - 42 q^{20} + 3 q^{21} - 12 q^{22} - 4 q^{23} + 9 q^{24} - 7 q^{25} - 3 q^{26} - q^{27} + 5 q^{28} - 2 q^{29} - 2 q^{30} - 8 q^{31} - 35 q^{32} - 4 q^{33} - 38 q^{34} - 2 q^{35} + 17 q^{36} + 10 q^{37} + 12 q^{38} + 7 q^{39} + 14 q^{40} - 18 q^{41} - 3 q^{42} + 20 q^{44} - 6 q^{45} + 16 q^{46} - 15 q^{48} + 11 q^{49} + 23 q^{50} + 6 q^{51} + q^{52} - 10 q^{53} + 5 q^{54} - 8 q^{55} + 21 q^{56} + 12 q^{57} - 2 q^{58} - 36 q^{59} - 18 q^{60} + 18 q^{61} - 8 q^{62} + 3 q^{63} + 33 q^{64} - 2 q^{65} - 12 q^{66} - 4 q^{67} - 14 q^{68} + 16 q^{69} - 2 q^{70} + 24 q^{71} - 3 q^{72} - 2 q^{73} - 26 q^{74} + 17 q^{75} - 60 q^{76} + 4 q^{77} + q^{78} - 4 q^{79} - 50 q^{80} + 11 q^{81} + 42 q^{82} - 4 q^{83} + 5 q^{84} + 28 q^{85} + 44 q^{86} - 6 q^{87} - 108 q^{88} - 26 q^{89} - 2 q^{90} + 7 q^{91} + 8 q^{92} + 32 q^{93} + 48 q^{94} - 4 q^{95} + 33 q^{96} - 26 q^{97} + q^{98} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(273))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 13
273.2.a.a 273.a 1.a $1$ $2.180$ \(\Q\) None 273.2.a.a \(-2\) \(-1\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
273.2.a.b 273.a 1.a $1$ $2.180$ \(\Q\) None 273.2.a.b \(2\) \(1\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
273.2.a.c 273.a 1.a $2$ $2.180$ \(\Q(\sqrt{2}) \) None 273.2.a.c \(2\) \(-2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
273.2.a.d 273.a 1.a $3$ $2.180$ 3.3.316.1 None 273.2.a.d \(-2\) \(-3\) \(-3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
273.2.a.e 273.a 1.a $4$ $2.180$ 4.4.17428.1 None 273.2.a.e \(1\) \(4\) \(-3\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(273))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(273)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)