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

\( 64q + 4q^{3} + 64q^{9} + O(q^{10}) \) \( 64q + 4q^{3} + 64q^{9} - 16q^{11} + 8q^{19} - 16q^{23} + 64q^{25} + 4q^{27} + 32q^{29} + 8q^{31} + 32q^{37} + 8q^{39} - 16q^{41} - 8q^{43} + 64q^{49} + 32q^{53} + 16q^{57} - 16q^{65} - 8q^{67} - 16q^{71} + 16q^{73} + 4q^{75} + 32q^{77} - 8q^{79} + 64q^{81} - 48q^{89} + 16q^{91} - 16q^{97} - 16q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 17
4080.2.a.a \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-5\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-5q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
4080.2.a.b \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
4080.2.a.c \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4080.2.a.d \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
4080.2.a.e \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4080.2.a.f \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
4080.2.a.g \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
4080.2.a.h \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots\)
4080.2.a.i \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
4080.2.a.j \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-q^{15}+\cdots\)
4080.2.a.k \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
4080.2.a.l \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
4080.2.a.m \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
4080.2.a.n \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
4080.2.a.o \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{15}-q^{17}+\cdots\)
4080.2.a.p \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4080.2.a.q \(1\) \(32.579\) \(\Q\) None \(0\) \(-1\) \(1\) \(5\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+5q^{7}+q^{9}+5q^{11}-q^{15}+\cdots\)
4080.2.a.r \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
4080.2.a.s \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
4080.2.a.t \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-q^{17}+\cdots\)
4080.2.a.u \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4080.2.a.v \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
4080.2.a.w \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+3q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
4080.2.a.x \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4080.2.a.y \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
4080.2.a.z \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
4080.2.a.ba \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4080.2.a.bb \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}+q^{17}+\cdots\)
4080.2.a.bc \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+q^{9}+6q^{11}+2q^{13}+\cdots\)
4080.2.a.bd \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
4080.2.a.be \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
4080.2.a.bf \(1\) \(32.579\) \(\Q\) None \(0\) \(1\) \(1\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4080.2.a.bg \(2\) \(32.579\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4080.2.a.bh \(2\) \(32.579\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4080.2.a.bi \(2\) \(32.579\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(2\) \(-1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
4080.2.a.bj \(2\) \(32.579\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-2\) \(-5\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-2-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4080.2.a.bk \(2\) \(32.579\) \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
4080.2.a.bl \(2\) \(32.579\) \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-5q^{11}+(-3+\cdots)q^{13}+\cdots\)
4080.2.a.bm \(2\) \(32.579\) \(\Q(\sqrt{73}) \) None \(0\) \(2\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4080.2.a.bn \(2\) \(32.579\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}-2q^{13}+\cdots\)
4080.2.a.bo \(2\) \(32.579\) \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(2\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
4080.2.a.bp \(2\) \(32.579\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots\)
4080.2.a.bq \(2\) \(32.579\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(2+\beta )q^{13}+\cdots\)
4080.2.a.br \(3\) \(32.579\) 3.3.229.1 None \(0\) \(-3\) \(3\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4080.2.a.bs \(3\) \(32.579\) 3.3.316.1 None \(0\) \(3\) \(3\) \(-3\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
4080.2.a.bt \(4\) \(32.579\) 4.4.13768.1 None \(0\) \(-4\) \(-4\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(-1-\beta _{1})q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)

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

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