Properties

Label 273.2.c
Level $273$
Weight $2$
Character orbit 273.c
Rep. character $\chi_{273}(64,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $3$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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 40 16 24
Cusp forms 32 16 16
Eisenstein series 8 0 8

Trace form

\( 16q - 20q^{4} + 16q^{9} + O(q^{10}) \) \( 16q - 20q^{4} + 16q^{9} + 8q^{10} + 8q^{12} - 4q^{13} + 20q^{16} + 16q^{17} - 40q^{22} - 4q^{23} - 52q^{25} + 20q^{26} - 12q^{29} - 4q^{35} - 20q^{36} + 56q^{38} + 8q^{39} + 16q^{40} + 4q^{42} + 20q^{43} - 48q^{48} - 16q^{49} - 24q^{51} + 20q^{52} - 28q^{53} - 8q^{61} - 56q^{62} + 20q^{64} + 28q^{65} + 8q^{66} - 40q^{68} + 8q^{69} + 96q^{74} + 16q^{75} - 16q^{77} - 36q^{78} - 4q^{79} + 16q^{81} + 24q^{87} + 24q^{88} + 8q^{90} - 4q^{91} + 16q^{92} - 64q^{94} - 68q^{95} + O(q^{100}) \)

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.c.a \(2\) \(2.180\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+2iq^{2}+q^{3}-2q^{4}+3iq^{5}+2iq^{6}+\cdots\)
273.2.c.b \(6\) \(2.180\) 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) \(q-\beta _{4}q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
273.2.c.c \(8\) \(2.180\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-8\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)