Properties

Label 273.2.bl
Level $273$
Weight $2$
Character orbit 273.bl
Rep. character $\chi_{273}(88,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $38$
Newform subspaces $4$
Sturm bound $74$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bl (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: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 82 38 44
Cusp forms 66 38 28
Eisenstein series 16 0 16

Trace form

\( 38q - 6q^{3} + 20q^{4} - q^{7} + 38q^{9} + O(q^{10}) \) \( 38q - 6q^{3} + 20q^{4} - q^{7} + 38q^{9} + 16q^{10} - 8q^{12} - 2q^{13} - 24q^{14} - 14q^{16} - 4q^{17} - 24q^{20} + 7q^{21} + 10q^{22} + 4q^{23} + 25q^{25} + 22q^{26} - 6q^{27} - 44q^{28} + 3q^{31} - 14q^{35} + 20q^{36} - 15q^{37} + 16q^{38} - 8q^{39} + 14q^{40} + 18q^{41} - 22q^{42} + 4q^{43} - 12q^{44} + 12q^{46} - 36q^{47} + 18q^{48} - 29q^{49} - 102q^{50} - 44q^{52} - 8q^{53} + 30q^{55} - 6q^{56} - 48q^{59} - 36q^{60} - 34q^{61} - 40q^{62} - q^{63} - 20q^{64} + 8q^{65} + 16q^{66} - 8q^{68} - 20q^{69} - 36q^{70} + 18q^{71} + 42q^{73} + 12q^{74} - 13q^{75} + 58q^{77} - 18q^{78} + 19q^{79} + 38q^{81} - 12q^{82} + 50q^{84} - 48q^{85} - 36q^{86} + 18q^{87} + 24q^{88} - 48q^{89} + 16q^{90} + 29q^{91} + 140q^{92} + 3q^{93} - 104q^{94} + 20q^{95} + 30q^{96} + 27q^{97} - 30q^{98} + O(q^{100}) \)

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.bl.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) None \(3\) \(-2\) \(6\) \(1\) \(q+(2-\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\)
273.2.bl.b \(4\) \(2.180\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(3\) \(4\) \(-6\) \(0\) \(q+(1-\beta _{3})q^{2}+q^{3}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots\)
273.2.bl.c \(12\) \(2.180\) 12.0.\(\cdots\).1 None \(-3\) \(12\) \(6\) \(3\) \(q+(-\beta _{1}-\beta _{6}+\beta _{8})q^{2}+q^{3}+(-1+\cdots)q^{4}+\cdots\)
273.2.bl.d \(20\) \(2.180\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-3\) \(-20\) \(-6\) \(-5\) \(q+\beta _{3}q^{2}-q^{3}+(\beta _{11}+\beta _{17})q^{4}+\beta _{8}q^{5}+\cdots\)

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

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