↑

Properties

Label 1656.2.a
Level $1656$
Weight $2$
Character orbit 1656.a
Rep. character $\chi_{1656}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $16$
Sturm bound $576$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1656 = 2^{3} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1656.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(576\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1656))\).

Total New Old
Modular forms 304 28 276
Cusp forms 273 28 245
Eisenstein series 31 0 31

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

\(2\)\(3\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(11\)
Minus space\(-\)\(17\)

Trace form

\( 28 q - 2 q^{5} - 2 q^{11} + 4 q^{13} + 8 q^{17} + 10 q^{19} + 40 q^{25} - 12 q^{31} + 2 q^{37} - 2 q^{43} + 4 q^{47} + 52 q^{49} - 6 q^{53} + 8 q^{55} + 8 q^{59} - 6 q^{61} - 8 q^{65} + 14 q^{67} + 20 q^{71}+ \cdots + 64 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1656))\) 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 23
1656.2.a.a 1656.a 1.a $1$ $13.223$ \(\Q\) None 552.2.a.d \(0\) \(0\) \(-4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{7}+2q^{13}+4q^{17}-6q^{19}+\cdots\)
1656.2.a.b 1656.a 1.a $1$ $13.223$ \(\Q\) None 552.2.a.c \(0\) \(0\) \(-2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
1656.2.a.c 1656.a 1.a $1$ $13.223$ \(\Q\) None 184.2.a.d \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-5q^{13}+6q^{17}+6q^{19}-q^{23}+\cdots\)
1656.2.a.d 1656.a 1.a $1$ $13.223$ \(\Q\) None 552.2.a.b \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+2q^{13}-8q^{17}+6q^{19}-q^{23}+\cdots\)
1656.2.a.e 1656.a 1.a $1$ $13.223$ \(\Q\) None 184.2.a.c \(0\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-6q^{11}-2q^{13}-6q^{17}-6q^{19}+\cdots\)
1656.2.a.f 1656.a 1.a $1$ $13.223$ \(\Q\) None 552.2.a.e \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}-2q^{13}+2q^{17}-4q^{19}+\cdots\)
1656.2.a.g 1656.a 1.a $1$ $13.223$ \(\Q\) None 184.2.a.b \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}+2q^{11}+7q^{13}+4q^{17}+\cdots\)
1656.2.a.h 1656.a 1.a $1$ $13.223$ \(\Q\) None 552.2.a.a \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+2q^{11}-2q^{13}+4q^{17}+\cdots\)
1656.2.a.i 1656.a 1.a $1$ $13.223$ \(\Q\) None 184.2.a.a \(0\) \(0\) \(4\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{7}+4q^{11}-5q^{13}+2q^{17}+\cdots\)
1656.2.a.j 1656.a 1.a $2$ $13.223$ \(\Q(\sqrt{17}) \) None 184.2.a.e \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+(-2+2\beta )q^{11}+(3-\beta )q^{13}+\cdots\)
1656.2.a.k 1656.a 1.a $2$ $13.223$ \(\Q(\sqrt{3}) \) None 1656.2.a.k \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(-1+\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
1656.2.a.l 1656.a 1.a $2$ $13.223$ \(\Q(\sqrt{5}) \) None 552.2.a.f \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+2q^{7}+(-1-\beta )q^{11}+\cdots\)
1656.2.a.m 1656.a 1.a $2$ $13.223$ \(\Q(\sqrt{3}) \) None 1656.2.a.k \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1-\beta )q^{7}+(-2-2\beta )q^{11}+\cdots\)
1656.2.a.n 1656.a 1.a $3$ $13.223$ 3.3.148.1 None 552.2.a.g \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(1+\beta _{1})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
1656.2.a.o 1656.a 1.a $4$ $13.223$ 4.4.44688.2 None 1656.2.a.o \(0\) \(0\) \(-4\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+(-\beta _{2}+\beta _{3})q^{11}+\cdots\)
1656.2.a.p 1656.a 1.a $4$ $13.223$ 4.4.44688.2 None 1656.2.a.o \(0\) \(0\) \(4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{5}-\beta _{1}q^{7}+(\beta _{2}-\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1656))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1656)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(828))\)\(^{\oplus 2}\)