Properties

Label 273.2.cd
Level $273$
Weight $2$
Character orbit 273.cd
Rep. character $\chi_{273}(44,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $136$
Newform subspaces $5$
Sturm bound $74$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(19\)

Dimensions

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

Total New Old
Modular forms 168 168 0
Cusp forms 136 136 0
Eisenstein series 32 32 0

Trace form

\( 136q - 4q^{3} - 16q^{6} - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 136q - 4q^{3} - 16q^{6} - 2q^{7} - 4q^{9} - 16q^{13} - 12q^{15} + 48q^{16} - 26q^{18} - 6q^{19} - 6q^{21} - 32q^{22} + 20q^{24} - 40q^{27} - 36q^{28} - 14q^{31} - 16q^{33} + 48q^{34} - 6q^{37} - 32q^{39} - 112q^{40} - 40q^{42} - 2q^{45} + 24q^{46} + 56q^{48} - 16q^{52} + 14q^{54} - 16q^{55} - 44q^{57} - 28q^{58} + 44q^{60} + 8q^{61} + 32q^{63} - 4q^{66} - 2q^{67} - 44q^{70} - 26q^{72} - 38q^{73} - 8q^{76} + 40q^{78} + 48q^{79} + 36q^{81} - 158q^{84} + 80q^{85} - 56q^{87} + 26q^{91} + 4q^{93} + 32q^{94} - 126q^{96} - 4q^{99} + O(q^{100}) \)

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.cd.a \(4\) \(2.180\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
273.2.cd.b \(4\) \(2.180\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
273.2.cd.c \(8\) \(2.180\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(-4\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(1-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
273.2.cd.d \(8\) \(2.180\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(4\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
273.2.cd.e \(112\) \(2.180\) None \(0\) \(-12\) \(0\) \(-4\)