Properties

Label 1064.2.a
Level $1064$
Weight $2$
Character orbit 1064.a
Rep. character $\chi_{1064}(1,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $9$
Sturm bound $320$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(320\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1064))\).

Total New Old
Modular forms 168 26 142
Cusp forms 153 26 127
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.

\(2\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(8\)
Minus space\(-\)\(18\)

Trace form

\( 26q + 4q^{5} + 22q^{9} + O(q^{10}) \) \( 26q + 4q^{5} + 22q^{9} + 12q^{11} - 4q^{13} + 24q^{15} + 4q^{17} + 18q^{25} + 24q^{27} - 4q^{29} - 16q^{31} + 12q^{35} + 28q^{37} + 8q^{39} - 4q^{41} + 4q^{43} + 44q^{45} + 48q^{47} + 26q^{49} + 16q^{51} + 28q^{53} - 16q^{55} - 4q^{57} + 16q^{59} + 12q^{61} + 8q^{65} - 16q^{67} + 24q^{69} + 24q^{71} - 12q^{73} - 16q^{75} - 8q^{77} + 8q^{79} - 6q^{81} - 48q^{83} - 8q^{85} - 20q^{89} - 8q^{91} - 8q^{93} - 44q^{97} + 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 19
1064.2.a.a \(2\) \(8.496\) \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
1064.2.a.b \(2\) \(8.496\) \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+(-1+\beta )q^{11}+\cdots\)
1064.2.a.c \(2\) \(8.496\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+(-1+2\beta )q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots\)
1064.2.a.d \(2\) \(8.496\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta q^{3}-q^{5}-q^{7}+(-2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots\)
1064.2.a.e \(2\) \(8.496\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(5\) \(2\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots\)
1064.2.a.f \(3\) \(8.496\) 3.3.1101.1 None \(0\) \(-1\) \(2\) \(3\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
1064.2.a.g \(4\) \(8.496\) 4.4.18097.1 None \(0\) \(0\) \(-3\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)
1064.2.a.h \(4\) \(8.496\) 4.4.25857.1 None \(0\) \(2\) \(1\) \(4\) \(-\) \(-\) \(-\) \(q+(1+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots\)
1064.2.a.i \(5\) \(8.496\) 5.5.10463409.1 None \(0\) \(0\) \(3\) \(-5\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(1-\beta _{4})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1064))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1064)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 2}\)