Properties

Label 273.2.ba
Level $273$
Weight $2$
Character orbit 273.ba
Rep. character $\chi_{273}(38,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $3$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(74\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

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

Total New Old
Modular forms 84 84 0
Cusp forms 68 68 0
Eisenstein series 16 16 0

Trace form

\( 68q - 6q^{3} - 36q^{4} - 6q^{9} + O(q^{10}) \) \( 68q - 6q^{3} - 36q^{4} - 6q^{9} - 12q^{10} + 6q^{12} - 40q^{16} - 24q^{22} + 18q^{25} - 22q^{30} + 68q^{36} + 9q^{39} - 108q^{40} + 24q^{42} - 20q^{43} - 6q^{49} + 28q^{51} + 30q^{52} + 24q^{61} + 90q^{66} - 90q^{75} - 68q^{78} - 10q^{79} + 42q^{81} + 120q^{82} + 60q^{87} + 12q^{88} - 39q^{91} + 168q^{94} + O(q^{100}) \)

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.ba.a \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-1\) \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
273.2.ba.b \(2\) \(2.180\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(1\) \(q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
273.2.ba.c \(64\) \(2.180\) None \(0\) \(-12\) \(0\) \(0\)