Properties

Label 273.2.bj
Level $273$
Weight $2$
Character orbit 273.bj
Rep. character $\chi_{273}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $4$
Sturm bound $74$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(74\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

Total New Old
Modular forms 84 36 48
Cusp forms 68 36 32
Eisenstein series 16 0 16

Trace form

\( 36q + 2q^{3} + 16q^{4} - 18q^{9} + O(q^{10}) \) \( 36q + 2q^{3} + 16q^{4} - 18q^{9} - 8q^{10} - 4q^{12} + 6q^{13} + 36q^{14} - 28q^{16} - 4q^{17} + 16q^{22} + 4q^{23} + 18q^{25} + 22q^{26} - 4q^{27} - 32q^{35} - 32q^{36} - 44q^{38} - q^{39} + 44q^{40} + 8q^{42} - 12q^{43} - 16q^{48} - 70q^{49} - 12q^{51} + 38q^{52} + 40q^{53} - 96q^{55} + 108q^{56} + 36q^{61} - 208q^{62} - 144q^{64} + 26q^{65} + 16q^{66} - 8q^{68} + 40q^{69} - 24q^{74} - 30q^{75} + 4q^{77} + 60q^{78} - 10q^{79} - 18q^{81} + 36q^{87} - 12q^{88} + 16q^{90} - 77q^{91} + 32q^{92} + 4q^{94} + 20q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
273.2.bj.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None \(-3\) \(1\) \(-6\) \(1\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+\zeta_{6}q^{4}+(-2+\cdots)q^{5}+\cdots\)
273.2.bj.b \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None \(3\) \(1\) \(6\) \(-1\) \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{3}+\zeta_{6}q^{4}+(2+2\zeta_{6})q^{5}+\cdots\)
273.2.bj.c \(16\) \(2.180\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-8\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{9})q^{2}-\beta _{10}q^{3}+(\beta _{10}-\beta _{11}+\cdots)q^{4}+\cdots\)
273.2.bj.d \(16\) \(2.180\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(8\) \(0\) \(0\) \(q-\beta _{8}q^{2}+\beta _{3}q^{3}+(\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)