Properties

Label 1083.2.a
Level $1083$
Weight $2$
Character orbit 1083.a
Rep. character $\chi_{1083}(1,\cdot)$
Character field $\Q$
Dimension $57$
Newform subspaces $19$
Sturm bound $253$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1083.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(253\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1083))\).

Total New Old
Modular forms 146 57 89
Cusp forms 107 57 50
Eisenstein series 39 0 39

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

\(3\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(14\)
\(+\)\(-\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(19\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(23\)
Minus space\(-\)\(34\)

Trace form

\( 57 q + 3 q^{2} - q^{3} + 57 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 57 q^{9} + O(q^{10}) \) \( 57 q + 3 q^{2} - q^{3} + 57 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 57 q^{9} - 2 q^{10} + q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + 69 q^{16} + 2 q^{17} + 3 q^{18} - 6 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 3 q^{24} + 59 q^{25} - 14 q^{26} - q^{27} - 4 q^{28} + 10 q^{29} + 10 q^{30} - 4 q^{31} - 21 q^{32} + 4 q^{33} + 10 q^{34} - 28 q^{35} + 57 q^{36} + 2 q^{37} + 2 q^{39} - 6 q^{40} + 10 q^{41} + 16 q^{42} + 4 q^{43} - 4 q^{44} + 2 q^{45} - 4 q^{46} - 8 q^{47} + q^{48} + 45 q^{49} + q^{50} + 2 q^{51} + 14 q^{52} + 2 q^{53} - q^{54} - 4 q^{55} - 30 q^{58} + 20 q^{59} - 10 q^{60} - 10 q^{61} - 28 q^{62} + 57 q^{64} + 24 q^{65} - 12 q^{66} - 12 q^{67} - 30 q^{68} - 12 q^{69} + 36 q^{70} + 3 q^{72} + 6 q^{73} + 14 q^{74} + 9 q^{75} - 8 q^{77} - 22 q^{78} - 16 q^{79} - 30 q^{80} + 57 q^{81} - 30 q^{82} - 40 q^{83} - 16 q^{84} - 40 q^{85} + 6 q^{87} - 2 q^{89} - 2 q^{90} + 28 q^{91} - 28 q^{92} - 20 q^{93} - 24 q^{94} - 5 q^{96} + 2 q^{97} + 47 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 19
1083.2.a.a 1083.a 1.a $1$ $8.648$ \(\Q\) None 57.2.a.c \(-1\) \(-1\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
1083.2.a.b 1083.a 1.a $1$ $8.648$ \(\Q\) None 57.2.e.a \(-1\) \(1\) \(0\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
1083.2.a.c 1083.a 1.a $1$ $8.648$ \(\Q\) None 57.2.e.a \(1\) \(-1\) \(0\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
1083.2.a.d 1083.a 1.a $1$ $8.648$ \(\Q\) None 57.2.a.b \(2\) \(-1\) \(1\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
1083.2.a.e 1083.a 1.a $1$ $8.648$ \(\Q\) None 57.2.a.a \(2\) \(1\) \(-3\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
1083.2.a.f 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None 1083.2.a.f \(-3\) \(2\) \(1\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+\beta q^{5}+\cdots\)
1083.2.a.g 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{17}) \) None 1083.2.a.g \(-1\) \(-2\) \(-3\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
1083.2.a.h 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None 1083.2.a.h \(-1\) \(2\) \(-1\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(1-3\beta )q^{5}+\cdots\)
1083.2.a.i 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None 1083.2.a.h \(1\) \(-2\) \(-1\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-3\beta )q^{5}+\cdots\)
1083.2.a.j 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{17}) \) None 1083.2.a.g \(1\) \(2\) \(-3\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
1083.2.a.k 1083.a 1.a $2$ $8.648$ \(\Q(\sqrt{5}) \) None 1083.2.a.f \(3\) \(-2\) \(1\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1083.2.a.l 1083.a 1.a $3$ $8.648$ 3.3.564.1 None 57.2.e.b \(-1\) \(3\) \(2\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1083.2.a.m 1083.a 1.a $3$ $8.648$ \(\Q(\zeta_{18})^+\) None 57.2.i.a \(0\) \(-3\) \(-3\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1083.2.a.n 1083.a 1.a $3$ $8.648$ \(\Q(\zeta_{18})^+\) None 57.2.i.a \(0\) \(3\) \(-3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1083.2.a.o 1083.a 1.a $3$ $8.648$ 3.3.564.1 None 57.2.e.b \(1\) \(-3\) \(2\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
1083.2.a.p 1083.a 1.a $6$ $8.648$ 6.6.6357609.1 None 57.2.i.b \(0\) \(-6\) \(9\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1083.2.a.q 1083.a 1.a $6$ $8.648$ 6.6.6357609.1 None 57.2.i.b \(0\) \(6\) \(9\) \(9\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1083.2.a.r 1083.a 1.a $8$ $8.648$ 8.8.9764000000.1 None 1083.2.a.r \(-4\) \(-8\) \(-2\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1083.2.a.s 1083.a 1.a $8$ $8.648$ 8.8.9764000000.1 None 1083.2.a.r \(4\) \(8\) \(-2\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1083))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1083)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 2}\)