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Properties

Label 1092.2.cl
Level $1092$
Weight $2$
Character orbit 1092.cl
Rep. character $\chi_{1092}(857,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $3$
Sturm bound $448$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1092.cl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(448\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1092, [\chi])\).

Total New Old
Modular forms 472 76 396
Cusp forms 424 76 348
Eisenstein series 48 0 48

Trace form

\( 76 q - 4 q^{9} + O(q^{10}) \) \( 76 q - 4 q^{9} + 42 q^{25} - 9 q^{39} + 20 q^{43} - 14 q^{49} - 18 q^{51} + 36 q^{61} - 54 q^{75} - 34 q^{79} - 4 q^{81} - 48 q^{87} + 7 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1092, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1092.2.cl.a 1092.cl 273.aa $2$ $8.720$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(-5\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1092.2.cl.b 1092.cl 273.aa $2$ $8.720$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(5\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1092.2.cl.c 1092.cl 273.aa $72$ $8.720$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1092, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1092, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)