Properties

Label 2520.2.a
Level $2520$
Weight $2$
Character orbit 2520.a
Rep. character $\chi_{2520}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $25$
Sturm bound $1152$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(1152\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2520))\).

Total New Old
Modular forms 608 30 578
Cusp forms 545 30 515
Eisenstein series 63 0 63

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.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(12\)
Minus space\(-\)\(18\)

Trace form

\( 30q + O(q^{10}) \) \( 30q + 4q^{11} - 12q^{17} - 12q^{19} - 8q^{23} + 30q^{25} - 6q^{35} - 4q^{37} - 20q^{41} + 8q^{43} + 16q^{47} + 30q^{49} + 4q^{53} + 8q^{55} + 20q^{59} + 16q^{61} + 8q^{65} + 44q^{73} + 8q^{77} + 44q^{79} + 20q^{83} - 4q^{85} + 28q^{89} + 8q^{91} - 4q^{95} + 76q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2520))\) 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
2520.2.a.a \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
2520.2.a.b \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}-4q^{11}+6q^{13}+4q^{17}+\cdots\)
2520.2.a.c \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}-2q^{11}-2q^{13}+6q^{17}+\cdots\)
2520.2.a.d \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}+2q^{13}-2q^{17}+q^{25}+\cdots\)
2520.2.a.e \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{5}-q^{7}+2q^{11}-6q^{13}-2q^{17}+\cdots\)
2520.2.a.f \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{5}-q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
2520.2.a.g \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
2520.2.a.h \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}+2q^{11}-2q^{13}-2q^{17}+\cdots\)
2520.2.a.i \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+5q^{11}-5q^{13}+7q^{17}+\cdots\)
2520.2.a.j \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
2520.2.a.k \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}-2q^{11}-6q^{13}+2q^{17}+\cdots\)
2520.2.a.l \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
2520.2.a.m \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}+2q^{11}-2q^{13}-6q^{17}+\cdots\)
2520.2.a.n \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+4q^{11}-6q^{13}+2q^{17}+\cdots\)
2520.2.a.o \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{7}+4q^{11}+6q^{13}-4q^{17}+\cdots\)
2520.2.a.p \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+5q^{11}+q^{13}-3q^{17}+\cdots\)
2520.2.a.q \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
2520.2.a.r \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
2520.2.a.s \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
2520.2.a.t \(1\) \(20.122\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{5}+q^{7}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
2520.2.a.u \(2\) \(20.122\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{5}+q^{7}+(-1-\beta )q^{11}+2q^{13}+\cdots\)
2520.2.a.v \(2\) \(20.122\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
2520.2.a.w \(2\) \(20.122\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}+\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
2520.2.a.x \(2\) \(20.122\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{5}-q^{7}+(-3-\beta )q^{11}+(1+\beta )q^{13}+\cdots\)
2520.2.a.y \(2\) \(20.122\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{5}+q^{7}+(1+\beta )q^{11}+2q^{13}+(1+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2520))\) into lower level spaces

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