Properties

Label 5780.2.a
Level $5780$
Weight $2$
Character orbit 5780.a
Rep. character $\chi_{5780}(1,\cdot)$
Character field $\Q$
Dimension $91$
Newform subspaces $19$
Sturm bound $1836$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5780 = 2^{2} \cdot 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5780.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(1836\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5780))\).

Total New Old
Modular forms 972 91 881
Cusp forms 865 91 774
Eisenstein series 107 0 107

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

\(2\)\(5\)\(17\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(27\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(27\)
Plus space\(+\)\(37\)
Minus space\(-\)\(54\)

Trace form

\( 91q + 2q^{3} - q^{5} + 2q^{7} + 91q^{9} + O(q^{10}) \) \( 91q + 2q^{3} - q^{5} + 2q^{7} + 91q^{9} - 4q^{11} + 2q^{13} - 2q^{15} + 4q^{19} - 4q^{21} - 14q^{23} + 91q^{25} + 8q^{27} + 2q^{29} - 12q^{31} + 12q^{33} - 2q^{35} + 6q^{37} + 24q^{39} - 18q^{41} + 14q^{43} - 9q^{45} + 14q^{47} + 91q^{49} + 2q^{53} + 24q^{57} - 6q^{61} - 2q^{63} - 6q^{65} + 22q^{67} + 28q^{69} - 8q^{71} + 2q^{73} + 2q^{75} + 16q^{77} + 87q^{81} - 2q^{83} + 12q^{87} - 2q^{89} - 8q^{91} + 20q^{93} - 4q^{95} + 14q^{97} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5780))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 17
5780.2.a.a \(1\) \(46.154\) \(\Q\) None \(0\) \(-2\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{3}+q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots\)
5780.2.a.b \(1\) \(46.154\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q-q^{5}+2q^{7}-3q^{9}-q^{11}+3q^{19}+\cdots\)
5780.2.a.c \(1\) \(46.154\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{5}-2q^{7}-3q^{9}+q^{11}+3q^{19}+\cdots\)
5780.2.a.d \(1\) \(46.154\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(-\) \(+\) \(q+q^{5}+4q^{7}-3q^{9}-2q^{11}-6q^{13}+\cdots\)
5780.2.a.e \(1\) \(46.154\) \(\Q\) None \(0\) \(2\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+5q^{11}+\cdots\)
5780.2.a.f \(1\) \(46.154\) \(\Q\) None \(0\) \(2\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
5780.2.a.g \(2\) \(46.154\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+(-1+\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+\cdots\)
5780.2.a.h \(2\) \(46.154\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}+q^{5}+(1+\beta )q^{7}+2\beta q^{9}+\cdots\)
5780.2.a.i \(3\) \(46.154\) 3.3.1524.1 None \(0\) \(-2\) \(3\) \(-4\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
5780.2.a.j \(3\) \(46.154\) 3.3.404.1 None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{3}-q^{5}+\beta _{2}q^{7}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots\)
5780.2.a.k \(3\) \(46.154\) 3.3.1524.1 None \(0\) \(2\) \(-3\) \(4\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{3}-q^{5}+(1+\beta _{1})q^{7}+(3+\cdots)q^{9}+\cdots\)
5780.2.a.l \(6\) \(46.154\) 6.6.14414517.1 None \(0\) \(-3\) \(6\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{5}q^{3}+q^{5}-\beta _{2}q^{7}+\beta _{5}q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
5780.2.a.m \(6\) \(46.154\) 6.6.9521152.1 None \(0\) \(0\) \(-6\) \(4\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{5})q^{7}+\cdots\)
5780.2.a.n \(6\) \(46.154\) 6.6.9521152.1 None \(0\) \(0\) \(6\) \(-4\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots\)
5780.2.a.o \(6\) \(46.154\) 6.6.14414517.1 None \(0\) \(3\) \(-6\) \(0\) \(-\) \(+\) \(-\) \(q+\beta _{5}q^{3}-q^{5}+\beta _{2}q^{7}+\beta _{5}q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
5780.2.a.p \(12\) \(46.154\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(-12\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(2+\beta _{2})q^{9}+\cdots\)
5780.2.a.q \(12\) \(46.154\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-12\) \(-8\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{11})q^{7}+(1+\cdots)q^{9}+\cdots\)
5780.2.a.r \(12\) \(46.154\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(12\) \(8\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{11})q^{7}+(1+\beta _{8}+\cdots)q^{9}+\cdots\)
5780.2.a.s \(12\) \(46.154\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(12\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5780))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5780)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2890))\)\(^{\oplus 2}\)