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Properties

Label 1092.2.a
Level $1092$
Weight $2$
Character orbit 1092.a
Rep. character $\chi_{1092}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $8$
Sturm bound $448$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1092.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(448\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1092))\).

Total New Old
Modular forms 236 12 224
Cusp forms 213 12 201
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(13\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(+\)\(+\)\(14\)\(0\)\(14\)\(13\)\(0\)\(13\)\(1\)\(0\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(15\)\(0\)\(15\)\(13\)\(0\)\(13\)\(2\)\(0\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(15\)\(0\)\(15\)\(13\)\(0\)\(13\)\(2\)\(0\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(14\)\(0\)\(14\)\(12\)\(0\)\(12\)\(2\)\(0\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(16\)\(0\)\(16\)\(14\)\(0\)\(14\)\(2\)\(0\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(15\)\(0\)\(15\)\(13\)\(0\)\(13\)\(2\)\(0\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(15\)\(0\)\(15\)\(13\)\(0\)\(13\)\(2\)\(0\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(16\)\(0\)\(16\)\(14\)\(0\)\(14\)\(2\)\(0\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(15\)\(1\)\(14\)\(14\)\(1\)\(13\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(14\)\(1\)\(13\)\(13\)\(1\)\(12\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(14\)\(2\)\(12\)\(13\)\(2\)\(11\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(15\)\(2\)\(13\)\(14\)\(2\)\(12\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(14\)\(1\)\(13\)\(13\)\(1\)\(12\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(15\)\(3\)\(12\)\(14\)\(3\)\(11\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(15\)\(2\)\(13\)\(14\)\(2\)\(12\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(14\)\(0\)\(14\)\(13\)\(0\)\(13\)\(1\)\(0\)\(1\)
Plus space\(+\)\(114\)\(4\)\(110\)\(103\)\(4\)\(99\)\(11\)\(0\)\(11\)
Minus space\(-\)\(122\)\(8\)\(114\)\(110\)\(8\)\(102\)\(12\)\(0\)\(12\)

Trace form

\( 12 q + 12 q^{9} + 8 q^{17} + 8 q^{19} - 4 q^{21} + 12 q^{23} + 8 q^{25} + 12 q^{29} + 8 q^{31} + 8 q^{33} + 4 q^{35} - 8 q^{41} + 20 q^{43} - 16 q^{47} + 12 q^{49} + 8 q^{51} - 4 q^{53} - 16 q^{55} - 8 q^{59}+ \cdots + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 13
1092.2.a.a 1092.a 1.a $1$ $8.720$ \(\Q\) None 1092.2.a.a \(0\) \(-1\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
1092.2.a.b 1092.a 1.a $1$ $8.720$ \(\Q\) None 1092.2.a.b \(0\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
1092.2.a.c 1092.a 1.a $1$ $8.720$ \(\Q\) None 1092.2.a.c \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+4q^{17}+\cdots\)
1092.2.a.d 1092.a 1.a $1$ $8.720$ \(\Q\) None 1092.2.a.d \(0\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
1092.2.a.e 1092.a 1.a $1$ $8.720$ \(\Q\) None 1092.2.a.e \(0\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
1092.2.a.f 1092.a 1.a $2$ $8.720$ \(\Q(\sqrt{5}) \) None 1092.2.a.f \(0\) \(-2\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
1092.2.a.g 1092.a 1.a $2$ $8.720$ \(\Q(\sqrt{33}) \) None 1092.2.a.g \(0\) \(2\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
1092.2.a.h 1092.a 1.a $3$ $8.720$ 3.3.1373.1 None 1092.2.a.h \(0\) \(3\) \(1\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1092))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1092)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)