Properties

Label 3640.2.a
Level $3640$
Weight $2$
Character orbit 3640.a
Rep. character $\chi_{3640}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $27$
Sturm bound $1344$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(1344\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3640))\).

Total New Old
Modular forms 688 72 616
Cusp forms 657 72 585
Eisenstein series 31 0 31

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

\(2\)\(5\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(32\)
Minus space\(-\)\(40\)

Trace form

\( 72 q + 8 q^{3} + 48 q^{9} + O(q^{10}) \) \( 72 q + 8 q^{3} + 48 q^{9} + 8 q^{11} - 24 q^{17} + 24 q^{19} + 72 q^{25} + 32 q^{27} - 48 q^{33} + 8 q^{37} - 8 q^{41} + 24 q^{43} + 72 q^{49} + 16 q^{51} + 16 q^{53} - 32 q^{57} + 24 q^{59} + 32 q^{61} + 8 q^{65} + 16 q^{67} + 16 q^{69} - 40 q^{71} - 24 q^{73} + 8 q^{75} + 24 q^{79} - 8 q^{81} - 24 q^{83} + 8 q^{85} + 16 q^{87} - 8 q^{89} + 48 q^{93} + 8 q^{95} - 40 q^{97} + 40 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3640))\) 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 5 7 13
3640.2.a.a 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(-2\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
3640.2.a.b 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
3640.2.a.c 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
3640.2.a.d 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
3640.2.a.e 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{9}-q^{13}+6q^{17}+\cdots\)
3640.2.a.f 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots\)
3640.2.a.g 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(2\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
3640.2.a.h 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(2\) \(-1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+q^{7}+q^{9}+6q^{11}-q^{13}+\cdots\)
3640.2.a.i 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(2\) \(1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
3640.2.a.j 3640.a 1.a $1$ $29.066$ \(\Q\) None \(0\) \(2\) \(1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
3640.2.a.k 3640.a 1.a $2$ $29.066$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}-q^{7}+(-2+\beta )q^{9}-q^{13}+\cdots\)
3640.2.a.l 3640.a 1.a $2$ $29.066$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(2\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+q^{7}+\beta q^{9}+(-2+2\beta )q^{11}+\cdots\)
3640.2.a.m 3640.a 1.a $2$ $29.066$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{9}+\beta q^{11}+q^{13}+\cdots\)
3640.2.a.n 3640.a 1.a $2$ $29.066$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(2\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-4\beta q^{11}+\cdots\)
3640.2.a.o 3640.a 1.a $3$ $29.066$ 3.3.229.1 None \(0\) \(-2\) \(-3\) \(-3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
3640.2.a.p 3640.a 1.a $3$ $29.066$ 3.3.1101.1 None \(0\) \(-1\) \(-3\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+q^{7}+(4-\beta _{1}+\beta _{2})q^{9}+\cdots\)
3640.2.a.q 3640.a 1.a $3$ $29.066$ 3.3.1573.1 None \(0\) \(1\) \(3\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
3640.2.a.r 3640.a 1.a $4$ $29.066$ 4.4.13676.1 None \(0\) \(-1\) \(-4\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}-q^{7}+(3+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
3640.2.a.s 3640.a 1.a $4$ $29.066$ 4.4.2225.1 None \(0\) \(-1\) \(4\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
3640.2.a.t 3640.a 1.a $4$ $29.066$ 4.4.24197.1 None \(0\) \(0\) \(-4\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+q^{7}+\beta _{2}q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
3640.2.a.u 3640.a 1.a $4$ $29.066$ 4.4.24197.1 None \(0\) \(0\) \(4\) \(-4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}-q^{7}+(4+\beta _{1})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
3640.2.a.v 3640.a 1.a $4$ $29.066$ 4.4.2225.1 None \(0\) \(1\) \(-4\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
3640.2.a.w 3640.a 1.a $4$ $29.066$ 4.4.23724.1 None \(0\) \(1\) \(-4\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+q^{7}+(1+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
3640.2.a.x 3640.a 1.a $4$ $29.066$ 4.4.4913.1 None \(0\) \(3\) \(-4\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}-q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
3640.2.a.y 3640.a 1.a $5$ $29.066$ 5.5.1194649.1 None \(0\) \(0\) \(-5\) \(5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
3640.2.a.z 3640.a 1.a $5$ $29.066$ 5.5.2112217.1 None \(0\) \(0\) \(5\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
3640.2.a.ba 3640.a 1.a $7$ $29.066$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(4\) \(7\) \(7\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+q^{7}+(2-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3640))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3640)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(910))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1820))\)\(^{\oplus 2}\)