Properties

Label 2064.2.a
Level $2064$
Weight $2$
Character orbit 2064.a
Rep. character $\chi_{2064}(1,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $27$
Sturm bound $704$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2064 = 2^{4} \cdot 3 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2064.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(704\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2064))\).

Total New Old
Modular forms 364 42 322
Cusp forms 341 42 299
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.

\(2\)\(3\)\(43\)FrickeDim
\(+\)\(+\)\(+\)$+$\(5\)
\(+\)\(+\)\(-\)$-$\(5\)
\(+\)\(-\)\(+\)$-$\(8\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(7\)
\(-\)\(+\)\(-\)$+$\(4\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(7\)
Plus space\(+\)\(15\)
Minus space\(-\)\(27\)

Trace form

\( 42 q + 4 q^{5} + 42 q^{9} + O(q^{10}) \) \( 42 q + 4 q^{5} + 42 q^{9} + 4 q^{13} + 4 q^{15} - 4 q^{17} + 8 q^{19} + 46 q^{25} + 4 q^{29} + 20 q^{31} + 8 q^{33} + 24 q^{35} + 4 q^{37} + 12 q^{41} - 6 q^{43} + 4 q^{45} + 12 q^{47} + 66 q^{49} + 8 q^{51} + 20 q^{53} - 12 q^{59} + 4 q^{61} - 8 q^{65} + 12 q^{67} - 16 q^{69} - 24 q^{71} - 12 q^{73} + 16 q^{77} + 16 q^{79} + 42 q^{81} + 16 q^{83} + 8 q^{85} + 12 q^{87} - 4 q^{89} + 24 q^{91} + 16 q^{93} + 64 q^{95} - 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2064))\) 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 3 43
2064.2.a.a 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
2064.2.a.b 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+3q^{7}+q^{9}+5q^{11}+\cdots\)
2064.2.a.c 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}-7q^{13}+\cdots\)
2064.2.a.d 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+2q^{11}+6q^{13}+6q^{17}+\cdots\)
2064.2.a.e 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
2064.2.a.f 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(-1\) \(2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
2064.2.a.g 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(-1\) \(3\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-5q^{7}+q^{9}+3q^{11}+\cdots\)
2064.2.a.h 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2064.2.a.i 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(-2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
2064.2.a.j 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(-2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
2064.2.a.k 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+2q^{7}+q^{9}+5q^{11}+\cdots\)
2064.2.a.l 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
2064.2.a.m 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
2064.2.a.n 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(1\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+5q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
2064.2.a.o 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
2064.2.a.p 2064.a 1.a $1$ $16.481$ \(\Q\) None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+7q^{13}+\cdots\)
2064.2.a.q 2064.a 1.a $2$ $16.481$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+(3-\beta )q^{7}+q^{9}+\cdots\)
2064.2.a.r 2064.a 1.a $2$ $16.481$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{5}+(1+2\beta )q^{7}+q^{9}+\cdots\)
2064.2.a.s 2064.a 1.a $2$ $16.481$ \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-5q^{11}+\cdots\)
2064.2.a.t 2064.a 1.a $2$ $16.481$ \(\Q(\sqrt{41}) \) None \(0\) \(-2\) \(4\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
2064.2.a.u 2064.a 1.a $2$ $16.481$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
2064.2.a.v 2064.a 1.a $2$ $16.481$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}+(-1-2\beta )q^{7}+q^{9}+\cdots\)
2064.2.a.w 2064.a 1.a $2$ $16.481$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots\)
2064.2.a.x 2064.a 1.a $3$ $16.481$ 3.3.568.1 None \(0\) \(-3\) \(-4\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2064.2.a.y 2064.a 1.a $3$ $16.481$ 3.3.568.1 None \(0\) \(-3\) \(4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
2064.2.a.z 2064.a 1.a $3$ $16.481$ 3.3.3592.1 None \(0\) \(3\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
2064.2.a.ba 2064.a 1.a $3$ $16.481$ 3.3.568.1 None \(0\) \(3\) \(4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2064))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2064)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(258))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(344))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(516))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(688))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1032))\)\(^{\oplus 2}\)