Properties

Label 4080.2.a
Level $4080$
Weight $2$
Character orbit 4080.a
Rep. character $\chi_{4080}(1,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $46$
Sturm bound $1728$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4080 = 2^{4} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4080.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 46 \)
Sturm bound: \(1728\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4080))\).

Total New Old
Modular forms 888 64 824
Cusp forms 841 64 777
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.

\(2\)\(3\)\(5\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(26\)
Minus space\(-\)\(38\)

Trace form

\( 64 q + 4 q^{3} + 64 q^{9} - 16 q^{11} + 8 q^{19} - 16 q^{23} + 64 q^{25} + 4 q^{27} + 32 q^{29} + 8 q^{31} + 32 q^{37} + 8 q^{39} - 16 q^{41} - 8 q^{43} + 64 q^{49} + 32 q^{53} + 16 q^{57} - 16 q^{65} - 8 q^{67}+ \cdots - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4080))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 17
4080.2.a.a 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.g \(0\) \(-1\) \(-1\) \(-5\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-5q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
4080.2.a.b 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.l \(0\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
4080.2.a.c 4080.a 1.a $1$ $32.579$ \(\Q\) None 510.2.a.f \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4080.2.a.d 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.f \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
4080.2.a.e 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.k \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4080.2.a.f 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.e \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
4080.2.a.g 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.j \(0\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
4080.2.a.h 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.i \(0\) \(-1\) \(-1\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots\)
4080.2.a.i 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.h \(0\) \(-1\) \(-1\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
4080.2.a.j 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.q \(0\) \(-1\) \(1\) \(-3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-q^{15}+\cdots\)
4080.2.a.k 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.p \(0\) \(-1\) \(1\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
4080.2.a.l 4080.a 1.a $1$ $32.579$ \(\Q\) None 510.2.a.g \(0\) \(-1\) \(1\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
4080.2.a.m 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.o \(0\) \(-1\) \(1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
4080.2.a.n 4080.a 1.a $1$ $32.579$ \(\Q\) None 510.2.a.b \(0\) \(-1\) \(1\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
4080.2.a.o 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.n \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{15}-q^{17}+\cdots\)
4080.2.a.p 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.m \(0\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4080.2.a.q 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.h \(0\) \(-1\) \(1\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+5q^{7}+q^{9}+5q^{11}-q^{15}+\cdots\)
4080.2.a.r 4080.a 1.a $1$ $32.579$ \(\Q\) None 510.2.a.d \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
4080.2.a.s 4080.a 1.a $1$ $32.579$ \(\Q\) None 510.2.a.a \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
4080.2.a.t 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.c \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-q^{17}+\cdots\)
4080.2.a.u 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.b \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4080.2.a.v 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.a \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
4080.2.a.w 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.a \(0\) \(1\) \(-1\) \(3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+3q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
4080.2.a.x 4080.a 1.a $1$ $32.579$ \(\Q\) None 510.2.a.c \(0\) \(1\) \(-1\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4080.2.a.y 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.d \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
4080.2.a.z 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.g \(0\) \(1\) \(1\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4080.2.a.ba 4080.a 1.a $1$ $32.579$ \(\Q\) None 510.2.a.e \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4080.2.a.bb 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.f \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}+q^{17}+\cdots\)
4080.2.a.bc 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.c \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}+6q^{11}+2q^{13}+\cdots\)
4080.2.a.bd 4080.a 1.a $1$ $32.579$ \(\Q\) None 1020.2.a.b \(0\) \(1\) \(1\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
4080.2.a.be 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.e \(0\) \(1\) \(1\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
4080.2.a.bf 4080.a 1.a $1$ $32.579$ \(\Q\) None 2040.2.a.d \(0\) \(1\) \(1\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4080.2.a.bg 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{17}) \) None 2040.2.a.v \(0\) \(-2\) \(-2\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4080.2.a.bh 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{33}) \) None 1020.2.a.j \(0\) \(-2\) \(2\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4080.2.a.bi 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{33}) \) None 2040.2.a.w \(0\) \(-2\) \(2\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
4080.2.a.bj 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{17}) \) None 2040.2.a.t \(0\) \(2\) \(-2\) \(-5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-2-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4080.2.a.bk 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{33}) \) None 1020.2.a.i \(0\) \(2\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
4080.2.a.bl 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{13}) \) None 255.2.a.a \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-5q^{11}+(-3+\cdots)q^{13}+\cdots\)
4080.2.a.bm 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{73}) \) None 2040.2.a.s \(0\) \(2\) \(-2\) \(1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4080.2.a.bn 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{17}) \) None 2040.2.a.r \(0\) \(2\) \(-2\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}-2q^{13}+\cdots\)
4080.2.a.bo 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{33}) \) None 2040.2.a.u \(0\) \(2\) \(2\) \(-1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
4080.2.a.bp 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{5}) \) None 255.2.a.b \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots\)
4080.2.a.bq 4080.a 1.a $2$ $32.579$ \(\Q(\sqrt{6}) \) None 510.2.a.h \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(2+\beta )q^{13}+\cdots\)
4080.2.a.br 4080.a 1.a $3$ $32.579$ 3.3.229.1 None 255.2.a.c \(0\) \(-3\) \(3\) \(-4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4080.2.a.bs 4080.a 1.a $3$ $32.579$ 3.3.316.1 None 2040.2.a.x \(0\) \(3\) \(3\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
4080.2.a.bt 4080.a 1.a $4$ $32.579$ 4.4.13768.1 None 255.2.a.d \(0\) \(-4\) \(-4\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1-\beta _{1})q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4080)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(340))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(680))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1020))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2040))\)\(^{\oplus 2}\)