Properties

Label 273.2.p
Level $273$
Weight $2$
Character orbit 273.p
Rep. character $\chi_{273}(34,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $40$
Newform subspaces $6$
Sturm bound $74$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(74\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 80 40 40
Cusp forms 64 40 24
Eisenstein series 16 0 16

Trace form

\( 40q + 4q^{7} - 40q^{9} + O(q^{10}) \) \( 40q + 4q^{7} - 40q^{9} + 16q^{11} - 24q^{14} - 64q^{16} + 12q^{21} + 16q^{22} + 4q^{28} + 8q^{29} + 40q^{32} - 16q^{35} - 24q^{39} - 24q^{42} + 16q^{44} - 8q^{46} + 40q^{50} - 56q^{53} + 40q^{57} + 48q^{58} - 16q^{60} - 4q^{63} + 16q^{65} - 56q^{67} - 16q^{70} + 24q^{71} - 32q^{74} + 32q^{78} + 24q^{79} + 40q^{81} + 36q^{84} - 40q^{85} + 48q^{86} + 36q^{91} + 176q^{92} + 40q^{93} + 120q^{98} - 16q^{99} + O(q^{100}) \)

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.p.a \(4\) \(2.180\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-8\) \(4\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-2+2\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.b \(4\) \(2.180\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(-4\) \(-4\) \(q-\beta _{2}q^{3}+2\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.c \(4\) \(2.180\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(4\) \(-4\) \(q-\beta _{2}q^{3}-2\beta _{2}q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
273.2.p.d \(4\) \(2.180\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(2-2\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.e \(12\) \(2.180\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-12\) \(12\) \(q+\beta _{8}q^{2}-\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots\)
273.2.p.f \(12\) \(2.180\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(12\) \(-4\) \(q+\beta _{8}q^{2}+\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots\)

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

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