Properties

Label 273.2.n
Level $273$
Weight $2$
Character orbit 273.n
Rep. character $\chi_{273}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $3$
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.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(74\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 80 56 24
Cusp forms 64 56 8
Eisenstein series 16 0 16

Trace form

\( 56q + 12q^{6} + O(q^{10}) \) \( 56q + 12q^{6} + 8q^{13} - 4q^{15} - 40q^{16} - 20q^{18} + 8q^{19} + 4q^{21} + 16q^{22} - 8q^{24} - 24q^{27} - 16q^{31} + 36q^{33} - 48q^{37} - 8q^{39} + 16q^{40} + 28q^{45} - 24q^{46} + 48q^{48} - 72q^{52} + 36q^{54} - 96q^{55} - 32q^{57} + 24q^{58} + 44q^{60} - 96q^{61} + 8q^{63} - 136q^{66} + 40q^{67} + 24q^{70} + 32q^{72} + 16q^{73} + 104q^{76} - 68q^{78} + 32q^{79} + 56q^{81} + 12q^{84} - 32q^{85} - 48q^{87} + 8q^{91} - 20q^{93} + 96q^{94} + 8q^{96} - 96q^{97} - 12q^{99} + O(q^{100}) \)

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.n.a \(4\) \(2.180\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(-8\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
273.2.n.b \(4\) \(2.180\) \(\Q(\zeta_{8})\) None \(4\) \(-4\) \(8\) \(0\) \(q+(1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
273.2.n.c \(48\) \(2.180\) None \(0\) \(8\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)