Properties

Label 273.2.by
Level $273$
Weight $2$
Character orbit 273.by
Rep. character $\chi_{273}(76,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $72$
Newform subspaces $4$
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.by (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
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 168 72 96
Cusp forms 136 72 64
Eisenstein series 32 0 32

Trace form

\( 72q - 2q^{7} + 36q^{9} + O(q^{10}) \) \( 72q - 2q^{7} + 36q^{9} - 16q^{11} + 48q^{14} + 24q^{16} - 10q^{21} - 16q^{22} - 56q^{28} - 8q^{29} - 40q^{32} - 8q^{35} - 28q^{37} + 8q^{39} - 12q^{42} - 12q^{43} - 16q^{44} - 112q^{46} - 30q^{49} + 176q^{50} - 112q^{53} - 180q^{56} + 48q^{57} + 48q^{58} - 104q^{60} - 4q^{63} + 32q^{65} + 16q^{67} - 56q^{70} - 24q^{71} - 16q^{74} - 8q^{78} + 48q^{79} - 36q^{81} + 20q^{84} - 56q^{85} - 48q^{86} + 216q^{88} + 86q^{91} - 80q^{92} + 12q^{93} + 96q^{95} + 36q^{98} + 16q^{99} + O(q^{100}) \)

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.by.a \(4\) \(2.180\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-2\) \(-2\) \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
273.2.by.b \(4\) \(2.180\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(0\) \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
273.2.by.c \(32\) \(2.180\) None \(-2\) \(0\) \(-2\) \(-2\)
273.2.by.d \(32\) \(2.180\) None \(-2\) \(0\) \(2\) \(2\)

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

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