Properties

Label 4560.2.a
Level $4560$
Weight $2$
Character orbit 4560.a
Rep. character $\chi_{4560}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $48$
Sturm bound $1920$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4560.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(1920\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4560))\).

Total New Old
Modular forms 984 72 912
Cusp forms 937 72 865
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.

\(2\)\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(28\)
Minus space\(-\)\(44\)

Trace form

\( 72q - 8q^{7} + 72q^{9} + O(q^{10}) \) \( 72q - 8q^{7} + 72q^{9} - 16q^{11} - 16q^{23} + 72q^{25} + 32q^{29} + 32q^{37} + 8q^{43} + 48q^{47} + 72q^{49} + 32q^{53} - 16q^{55} + 16q^{59} - 8q^{63} - 16q^{67} - 48q^{71} + 32q^{77} + 32q^{79} + 72q^{81} - 24q^{87} - 80q^{91} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4560))\) 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 19
4560.2.a.a \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
4560.2.a.b \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
4560.2.a.c \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
4560.2.a.d \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4560.2.a.e \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.f \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
4560.2.a.g \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.h \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}+q^{15}+\cdots\)
4560.2.a.i \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
4560.2.a.j \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
4560.2.a.k \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.l \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
4560.2.a.m \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
4560.2.a.n \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4560.2.a.o \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
4560.2.a.p \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
4560.2.a.q \(1\) \(36.412\) \(\Q\) None \(0\) \(-1\) \(1\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
4560.2.a.r \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{7}+q^{9}+6q^{11}-q^{15}+\cdots\)
4560.2.a.s \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.t \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
4560.2.a.u \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
4560.2.a.v \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
4560.2.a.w \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.x \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-4q^{7}+q^{9}-6q^{13}+q^{15}+\cdots\)
4560.2.a.y \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-2q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
4560.2.a.z \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
4560.2.a.ba \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.bb \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-6q^{17}+\cdots\)
4560.2.a.bc \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+2q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
4560.2.a.bd \(1\) \(36.412\) \(\Q\) None \(0\) \(1\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
4560.2.a.be \(2\) \(36.412\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-6\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(-3-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4560.2.a.bf \(2\) \(36.412\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
4560.2.a.bg \(2\) \(36.412\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
4560.2.a.bh \(2\) \(36.412\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4560.2.a.bi \(2\) \(36.412\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(6\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(3+\beta )q^{7}+q^{9}+(1-3\beta )q^{11}+\cdots\)
4560.2.a.bj \(2\) \(36.412\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4560.2.a.bk \(2\) \(36.412\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4560.2.a.bl \(2\) \(36.412\) \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4560.2.a.bm \(2\) \(36.412\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4560.2.a.bn \(2\) \(36.412\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
4560.2.a.bo \(2\) \(36.412\) \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4560.2.a.bp \(2\) \(36.412\) \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
4560.2.a.bq \(3\) \(36.412\) 3.3.1016.1 None \(0\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-\beta _{2}q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
4560.2.a.br \(3\) \(36.412\) 3.3.564.1 None \(0\) \(-3\) \(3\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
4560.2.a.bs \(3\) \(36.412\) 3.3.1772.1 None \(0\) \(-3\) \(3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
4560.2.a.bt \(3\) \(36.412\) 3.3.568.1 None \(0\) \(3\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+(1+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4560.2.a.bu \(3\) \(36.412\) 3.3.1524.1 None \(0\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
4560.2.a.bv \(3\) \(36.412\) 3.3.316.1 None \(0\) \(3\) \(3\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4560))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4560)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2280))\)\(^{\oplus 2}\)