Properties

Label 544.2.a
Level $544$
Weight $2$
Character orbit 544.a
Rep. character $\chi_{544}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $10$
Sturm bound $144$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 544 = 2^{5} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 544.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(144\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(544))\).

Total New Old
Modular forms 80 16 64
Cusp forms 65 16 49
Eisenstein series 15 0 15

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.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(10\)

Trace form

\( 16 q + 16 q^{9} + O(q^{10}) \) \( 16 q + 16 q^{9} - 16 q^{13} + 32 q^{25} + 16 q^{29} + 16 q^{33} - 16 q^{37} + 16 q^{41} - 32 q^{45} + 32 q^{49} - 48 q^{53} + 16 q^{57} - 16 q^{61} + 48 q^{65} - 16 q^{69} + 16 q^{77} - 16 q^{89} - 48 q^{93} - 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(544))\) 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
544.2.a.a 544.a 1.a $1$ $4.344$ \(\Q\) None \(0\) \(-2\) \(2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
544.2.a.b 544.a 1.a $1$ $4.344$ \(\Q\) None \(0\) \(-2\) \(4\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
544.2.a.c 544.a 1.a $1$ $4.344$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}-4q^{11}+2q^{13}-q^{17}+\cdots\)
544.2.a.d 544.a 1.a $1$ $4.344$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-q^{17}+\cdots\)
544.2.a.e 544.a 1.a $1$ $4.344$ \(\Q\) None \(0\) \(2\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
544.2.a.f 544.a 1.a $1$ $4.344$ \(\Q\) None \(0\) \(2\) \(4\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
544.2.a.g 544.a 1.a $2$ $4.344$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}-3\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
544.2.a.h 544.a 1.a $2$ $4.344$ \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+\beta q^{7}+7q^{9}+\beta q^{11}+\cdots\)
544.2.a.i 544.a 1.a $3$ $4.344$ 3.3.148.1 None \(0\) \(-2\) \(-2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
544.2.a.j 544.a 1.a $3$ $4.344$ 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 \(S_{2}^{\mathrm{old}}(\Gamma_0(544))\) into lower level spaces

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