Properties

Label 3264.2.a
Level $3264$
Weight $2$
Character orbit 3264.a
Rep. character $\chi_{3264}(1,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $46$
Sturm bound $1152$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3264.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 46 \)
Sturm bound: \(1152\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3264))\).

Total New Old
Modular forms 600 64 536
Cusp forms 553 64 489
Eisenstein series 47 0 47

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

\(2\)\(3\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(10\)
Plus space\(+\)\(26\)
Minus space\(-\)\(38\)

Trace form

\( 64 q + 64 q^{9} + O(q^{10}) \) \( 64 q + 64 q^{9} - 16 q^{13} - 16 q^{21} + 64 q^{25} + 32 q^{29} + 16 q^{37} + 64 q^{49} + 32 q^{53} - 16 q^{61} + 32 q^{77} + 64 q^{81} - 16 q^{93} + 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3264))\) 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 17
3264.2.a.a 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots\)
3264.2.a.b 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+q^{9}-q^{11}-3q^{13}+\cdots\)
3264.2.a.c 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
3264.2.a.d 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3264.2.a.e 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
3264.2.a.f 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-5q^{11}+5q^{13}+\cdots\)
3264.2.a.g 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+6q^{13}-q^{17}+\cdots\)
3264.2.a.h 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.i 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.j 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots\)
3264.2.a.k 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3264.2.a.l 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+5q^{11}+5q^{13}+\cdots\)
3264.2.a.m 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3264.2.a.n 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(3\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-4q^{7}+q^{9}-q^{11}+5q^{13}+\cdots\)
3264.2.a.o 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(3\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{7}+q^{9}-3q^{11}+\cdots\)
3264.2.a.p 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(-1\) \(4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+6q^{13}+\cdots\)
3264.2.a.q 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+q^{9}+q^{11}-3q^{13}+\cdots\)
3264.2.a.r 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(-3\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+4q^{7}+q^{9}-3q^{11}+\cdots\)
3264.2.a.s 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3264.2.a.t 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(-2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
3264.2.a.u 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+5q^{11}+5q^{13}+\cdots\)
3264.2.a.v 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
3264.2.a.w 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.x 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-2q^{13}-q^{17}+\cdots\)
3264.2.a.y 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+6q^{13}-q^{17}+\cdots\)
3264.2.a.z 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-5q^{11}+5q^{13}+\cdots\)
3264.2.a.ba 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3264.2.a.bb 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
3264.2.a.bc 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3264.2.a.bd 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+2q^{7}+q^{9}+3q^{11}+\cdots\)
3264.2.a.be 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(3\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+4q^{7}+q^{9}+q^{11}+5q^{13}+\cdots\)
3264.2.a.bf 3264.a 1.a $1$ $26.063$ \(\Q\) None \(0\) \(1\) \(4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-2q^{7}+q^{9}+6q^{13}+\cdots\)
3264.2.a.bg 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+q^{9}+(-1+\beta )q^{11}+\cdots\)
3264.2.a.bh 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-1\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta q^{5}+2q^{7}+q^{9}+\beta q^{11}+\cdots\)
3264.2.a.bi 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(-4+\cdots)q^{11}+\cdots\)
3264.2.a.bj 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(1\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+4q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
3264.2.a.bk 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(3\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+(2-2\beta )q^{7}+q^{9}+\cdots\)
3264.2.a.bl 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+q^{9}+(1-\beta )q^{11}+\cdots\)
3264.2.a.bm 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}-2q^{7}+q^{9}-\beta q^{11}+\cdots\)
3264.2.a.bn 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(1\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-4q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
3264.2.a.bo 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots\)
3264.2.a.bp 3264.a 1.a $2$ $26.063$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots\)
3264.2.a.bq 3264.a 1.a $3$ $26.063$ 3.3.316.1 None \(0\) \(-3\) \(-3\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
3264.2.a.br 3264.a 1.a $3$ $26.063$ 3.3.229.1 None \(0\) \(-3\) \(-1\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{5}+2q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
3264.2.a.bs 3264.a 1.a $3$ $26.063$ 3.3.316.1 None \(0\) \(3\) \(-3\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
3264.2.a.bt 3264.a 1.a $3$ $26.063$ 3.3.229.1 None \(0\) \(3\) \(-1\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}-2q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3264))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3264)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1632))\)\(^{\oplus 2}\)