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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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.2.c.a 273.c 13.b $2$ $2.180$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+q^{3}-2q^{4}+3iq^{5}+2iq^{6}+\cdots\)
273.2.c.b 273.c 13.b $6$ $2.180$ 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
273.2.c.c 273.c 13.b $8$ $2.180$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)

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

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