Properties

Label 1092.2.e
Level $1092$
Weight $2$
Character orbit 1092.e
Rep. character $\chi_{1092}(337,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $5$
Sturm bound $448$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1092.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(448\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 236 12 224
Cusp forms 212 12 200
Eisenstein series 24 0 24

Trace form

\( 12 q + 12 q^{9} + O(q^{10}) \) \( 12 q + 12 q^{9} - 8 q^{13} - 8 q^{17} + 28 q^{23} - 8 q^{25} + 12 q^{29} - 4 q^{35} - 8 q^{39} + 12 q^{43} - 12 q^{49} + 16 q^{51} - 20 q^{53} + 32 q^{55} - 32 q^{61} + 12 q^{65} + 8 q^{69} - 16 q^{77} + 52 q^{79} + 12 q^{81} - 8 q^{87} + 4 q^{91} - 12 q^{95} + O(q^{100}) \)

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.e.a 1092.e 13.b $2$ $8.720$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}+iq^{7}+q^{9}+2iq^{11}+\cdots\)
1092.2.e.b 1092.e 13.b $2$ $8.720$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+4iq^{5}+iq^{7}+q^{9}+(-3+2i)q^{13}+\cdots\)
1092.2.e.c 1092.e 13.b $2$ $8.720$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{7}+q^{9}+4iq^{11}+(-3+\cdots)q^{13}+\cdots\)
1092.2.e.d 1092.e 13.b $2$ $8.720$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}-iq^{7}+q^{9}+(2+3i)q^{13}+\cdots\)
1092.2.e.e 1092.e 13.b $4$ $8.720$ \(\Q(i, \sqrt{17})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1092, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)