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Properties

Label 1092.2.bd
Level $1092$
Weight $2$
Character orbit 1092.bd
Rep. character $\chi_{1092}(797,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $3$
Sturm bound $448$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1092.bd (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: \(3\)
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

\( 76 q + 3 q^{7} + 2 q^{9} + O(q^{10}) \) \( 76 q + 3 q^{7} + 2 q^{9} + 6 q^{15} - 84 q^{25} - 6 q^{39} - 10 q^{43} + 7 q^{49} - 24 q^{51} - 12 q^{63} + 66 q^{67} + 20 q^{79} + 2 q^{81} - 12 q^{85} - 11 q^{91} + 48 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1092.2.bd.a 1092.bd 273.u $2$ $8.720$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 1092.2.bd.a \(0\) \(-3\) \(0\) \(1\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1092.2.bd.b 1092.bd 273.u $2$ $8.720$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 1092.2.bd.a \(0\) \(3\) \(0\) \(-4\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-1-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
1092.2.bd.c 1092.bd 273.u $72$ $8.720$ None 1092.2.bd.c \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$

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

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