Properties

Label 1088.2.a
Level $1088$
Weight $2$
Character orbit 1088.a
Rep. character $\chi_{1088}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $22$
Sturm bound $288$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1088.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(288\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1088))\).

Total New Old
Modular forms 156 32 124
Cusp forms 133 32 101
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.

\(2\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(20\)

Trace form

\( 32 q + 32 q^{9} + O(q^{10}) \) \( 32 q + 32 q^{9} + 16 q^{13} + 16 q^{21} + 32 q^{25} - 16 q^{29} + 48 q^{45} + 32 q^{49} + 32 q^{53} + 16 q^{61} + 48 q^{69} - 16 q^{77} - 32 q^{89} + 16 q^{93} - 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 17
1088.2.a.a 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(-2\) \(-4\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
1088.2.a.b 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(-2\) \(-2\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
1088.2.a.c 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(-2\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}-2q^{11}+6q^{13}-q^{17}+\cdots\)
1088.2.a.d 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(-2\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1088.2.a.e 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(-2\) \(2\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots\)
1088.2.a.f 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+4q^{11}-2q^{13}-q^{17}+\cdots\)
1088.2.a.g 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-4q^{11}-2q^{13}-q^{17}+\cdots\)
1088.2.a.h 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
1088.2.a.i 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-3q^{9}+2q^{13}+q^{17}+\cdots\)
1088.2.a.j 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(2\) \(-4\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
1088.2.a.k 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
1088.2.a.l 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(2\) \(0\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1088.2.a.m 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}+2q^{11}+6q^{13}-q^{17}+\cdots\)
1088.2.a.n 1088.a 1.a $1$ $8.688$ \(\Q\) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots\)
1088.2.a.o 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-4\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-2q^{5}+(-1-\beta )q^{7}+\cdots\)
1088.2.a.p 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-2\beta q^{5}+(-1+\beta )q^{7}+\cdots\)
1088.2.a.q 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}+3\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
1088.2.a.r 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}-\beta q^{7}+7q^{9}+\beta q^{11}+\cdots\)
1088.2.a.s 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-2q^{5}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
1088.2.a.t 1088.a 1.a $2$ $8.688$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+2\beta q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1088.2.a.u 1088.a 1.a $3$ $8.688$ 3.3.148.1 None \(0\) \(-2\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
1088.2.a.v 1088.a 1.a $3$ $8.688$ 3.3.148.1 None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1088))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1088)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 2}\)