Properties

Label 1856.2.a
Level $1856$
Weight $2$
Character orbit 1856.a
Rep. character $\chi_{1856}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $29$
Sturm bound $480$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(480\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1856))\).

Total New Old
Modular forms 252 56 196
Cusp forms 229 56 173
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.

\(2\)\(29\)FrickeDim.
\(+\)\(+\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(17\)
\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(22\)
Minus space\(-\)\(34\)

Trace form

\( 56 q + 56 q^{9} + O(q^{10}) \) \( 56 q + 56 q^{9} + 16 q^{13} + 16 q^{21} + 56 q^{25} - 16 q^{33} + 16 q^{37} - 16 q^{41} + 48 q^{45} + 56 q^{49} + 48 q^{53} - 16 q^{57} - 16 q^{61} + 16 q^{69} + 48 q^{77} + 40 q^{81} + 16 q^{85} + 64 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1856))\) 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 29
1856.2.a.a 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-3\) \(-3\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-3q^{5}-4q^{7}+6q^{9}-q^{11}+\cdots\)
1856.2.a.b 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-3\) \(3\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+3q^{5}+2q^{7}+6q^{9}-q^{11}+\cdots\)
1856.2.a.c 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-2\) \(2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots\)
1856.2.a.d 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-4q^{7}-2q^{9}-3q^{11}+\cdots\)
1856.2.a.e 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots\)
1856.2.a.f 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}-2q^{9}-3q^{11}+\cdots\)
1856.2.a.g 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+5q^{11}-q^{13}+\cdots\)
1856.2.a.h 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(-1\) \(3\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{7}-2q^{9}-3q^{11}+\cdots\)
1856.2.a.i 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(1\) \(-3\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+4q^{7}-2q^{9}+3q^{11}+\cdots\)
1856.2.a.j 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+3q^{11}+\cdots\)
1856.2.a.k 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+3q^{11}+\cdots\)
1856.2.a.l 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots\)
1856.2.a.m 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(1\) \(3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\)
1856.2.a.n 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(2\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots\)
1856.2.a.o 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(3\) \(-3\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-3q^{5}+4q^{7}+6q^{9}+q^{11}+\cdots\)
1856.2.a.p 1856.a 1.a $1$ $14.820$ \(\Q\) None \(0\) \(3\) \(3\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+3q^{5}-2q^{7}+6q^{9}+q^{11}+\cdots\)
1856.2.a.q 1856.a 1.a $2$ $14.820$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+2q^{7}-2\beta q^{9}+\cdots\)
1856.2.a.r 1856.a 1.a $2$ $14.820$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}-2\beta q^{9}+\cdots\)
1856.2.a.s 1856.a 1.a $2$ $14.820$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(1+2\beta )q^{5}+4q^{7}+\cdots\)
1856.2.a.t 1856.a 1.a $2$ $14.820$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-6\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-3q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots\)
1856.2.a.u 1856.a 1.a $2$ $14.820$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-2q^{7}+2\beta q^{9}+(1+\cdots)q^{11}+\cdots\)
1856.2.a.v 1856.a 1.a $2$ $14.820$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1-2\beta )q^{5}-4q^{7}+2\beta q^{9}+\cdots\)
1856.2.a.w 1856.a 1.a $2$ $14.820$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+2\beta q^{7}+2\beta q^{9}+\cdots\)
1856.2.a.x 1856.a 1.a $3$ $14.820$ 3.3.568.1 None \(0\) \(-2\) \(-4\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(2+\cdots)q^{9}+\cdots\)
1856.2.a.y 1856.a 1.a $3$ $14.820$ 3.3.568.1 None \(0\) \(2\) \(-4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\)
1856.2.a.z 1856.a 1.a $4$ $14.820$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(8\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(2-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1856.2.a.ba 1856.a 1.a $5$ $14.820$ 5.5.230224.1 None \(0\) \(-4\) \(2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-\beta _{4}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1856.2.a.bb 1856.a 1.a $5$ $14.820$ 5.5.230224.1 None \(0\) \(4\) \(2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-\beta _{4}q^{5}+(-1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1856.2.a.bc 1856.a 1.a $6$ $14.820$ 6.6.68772992.1 None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+(-1-\beta _{3})q^{5}-\beta _{1}q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1856))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1856)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(928))\)\(^{\oplus 2}\)