Properties

Label 5040.2.a
Level $5040$
Weight $2$
Character orbit 5040.a
Rep. character $\chi_{5040}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $51$
Sturm bound $2304$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5040.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 51 \)
Sturm bound: \(2304\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5040))\).

Total New Old
Modular forms 1200 60 1140
Cusp forms 1105 60 1045
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(27\)
Minus space\(-\)\(33\)

Trace form

\( 60q + 2q^{7} + O(q^{10}) \) \( 60q + 2q^{7} + 4q^{11} - 8q^{17} - 8q^{19} - 8q^{23} + 60q^{25} - 8q^{29} - 8q^{31} + 6q^{35} - 8q^{37} + 8q^{41} - 8q^{43} - 24q^{47} + 60q^{49} - 8q^{53} - 48q^{59} + 16q^{61} - 8q^{67} - 8q^{71} + 24q^{73} - 8q^{77} - 28q^{79} - 24q^{83} + 16q^{85} + 8q^{89} - 16q^{95} + 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5040))\) 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 7
5040.2.a.a \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-5q^{11}-5q^{13}+7q^{17}+\cdots\)
5040.2.a.b \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.c \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.d \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-6q^{13}-2q^{17}+8q^{19}+\cdots\)
5040.2.a.e \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
5040.2.a.f \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.g \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}+2q^{13}+6q^{17}-8q^{19}+\cdots\)
5040.2.a.h \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}+3q^{11}-q^{13}+3q^{17}+\cdots\)
5040.2.a.i \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.j \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.k \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.l \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.m \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}-4q^{11}+2q^{17}+6q^{19}+\cdots\)
5040.2.a.n \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.o \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}-2q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.p \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+2q^{13}-2q^{17}+q^{25}+\cdots\)
5040.2.a.q \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.r \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.s \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.t \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.u \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
5040.2.a.v \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots\)
5040.2.a.w \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}-4q^{13}+6q^{17}-2q^{19}+\cdots\)
5040.2.a.x \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
5040.2.a.y \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
5040.2.a.z \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.ba \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+2q^{13}+6q^{17}+4q^{19}+\cdots\)
5040.2.a.bb \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
5040.2.a.bc \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+6q^{11}-4q^{13}-6q^{17}+\cdots\)
5040.2.a.bd \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-5q^{11}-3q^{13}+q^{17}+\cdots\)
5040.2.a.be \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
5040.2.a.bf \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bg \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bh \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.bi \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
5040.2.a.bj \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
5040.2.a.bk \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}+2q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bl \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+2q^{11}+4q^{13}-6q^{17}+\cdots\)
5040.2.a.bm \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.bn \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bo \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}+4q^{11}-2q^{17}+6q^{19}+\cdots\)
5040.2.a.bp \(1\) \(40.245\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.bq \(2\) \(40.245\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
5040.2.a.br \(2\) \(40.245\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}+\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
5040.2.a.bs \(2\) \(40.245\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}+(1+\beta )q^{11}+2q^{13}+(-1+\cdots)q^{17}+\cdots\)
5040.2.a.bt \(2\) \(40.245\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+\beta q^{11}+(2+\beta )q^{13}+(2+\cdots)q^{17}+\cdots\)
5040.2.a.bu \(2\) \(40.245\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}+(2+\beta )q^{11}+(-2+\beta )q^{13}+\cdots\)
5040.2.a.bv \(2\) \(40.245\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}+(-1-\beta )q^{11}+2q^{13}+\cdots\)
5040.2.a.bw \(2\) \(40.245\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+(2+\beta )q^{11}+\beta q^{13}+2q^{17}+\cdots\)
5040.2.a.bx \(2\) \(40.245\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}+(-2+\beta )q^{11}+(-2-\beta )q^{13}+\cdots\)
5040.2.a.by \(2\) \(40.245\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+(4-\beta )q^{11}+(2-\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1260))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2520))\)\(^{\oplus 2}\)