Properties

Label 2480.2.a
Level $2480$
Weight $2$
Character orbit 2480.a
Rep. character $\chi_{2480}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $28$
Sturm bound $768$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2480 = 2^{4} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2480.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(768\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2480))\).

Total New Old
Modular forms 396 60 336
Cusp forms 373 60 313
Eisenstein series 23 0 23

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

\(2\)\(5\)\(31\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(24\)
Minus space\(-\)\(36\)

Trace form

\( 60 q + 4 q^{7} + 68 q^{9} + O(q^{10}) \) \( 60 q + 4 q^{7} + 68 q^{9} + 8 q^{11} + 8 q^{17} + 8 q^{21} + 8 q^{23} + 60 q^{25} - 8 q^{29} - 12 q^{35} - 16 q^{37} - 24 q^{39} + 8 q^{43} + 8 q^{45} + 20 q^{47} + 68 q^{49} + 16 q^{51} - 16 q^{53} + 60 q^{63} + 8 q^{65} + 28 q^{67} + 8 q^{69} - 40 q^{71} + 24 q^{73} - 16 q^{77} + 40 q^{79} + 68 q^{81} + 16 q^{83} + 24 q^{87} + 8 q^{89} + 48 q^{91} + 16 q^{95} + 24 q^{97} + 48 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2480))\) 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 5 31
2480.2.a.a 2480.a 1.a $1$ $19.803$ \(\Q\) None 1240.2.a.g \(0\) \(-3\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}-2q^{7}+6q^{9}+2q^{11}+\cdots\)
2480.2.a.b 2480.a 1.a $1$ $19.803$ \(\Q\) None 155.2.a.b \(0\) \(-2\) \(-1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2480.2.a.c 2480.a 1.a $1$ $19.803$ \(\Q\) None 310.2.a.b \(0\) \(-2\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
2480.2.a.d 2480.a 1.a $1$ $19.803$ \(\Q\) None 1240.2.a.f \(0\) \(-2\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}+4q^{13}+2q^{15}+\cdots\)
2480.2.a.e 2480.a 1.a $1$ $19.803$ \(\Q\) None 1240.2.a.e \(0\) \(-2\) \(-1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
2480.2.a.f 2480.a 1.a $1$ $19.803$ \(\Q\) None 620.2.a.c \(0\) \(-1\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}-2q^{9}+2q^{13}+\cdots\)
2480.2.a.g 2480.a 1.a $1$ $19.803$ \(\Q\) None 1240.2.a.c \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}-2q^{11}+2q^{13}+8q^{19}+\cdots\)
2480.2.a.h 2480.a 1.a $1$ $19.803$ \(\Q\) None 1240.2.a.d \(0\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
2480.2.a.i 2480.a 1.a $1$ $19.803$ \(\Q\) None 620.2.a.b \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}+4q^{11}-4q^{13}+\cdots\)
2480.2.a.j 2480.a 1.a $1$ $19.803$ \(\Q\) None 1240.2.a.a \(0\) \(1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}-2q^{13}-q^{15}+\cdots\)
2480.2.a.k 2480.a 1.a $1$ $19.803$ \(\Q\) None 155.2.a.c \(0\) \(1\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}+4q^{11}-6q^{13}+\cdots\)
2480.2.a.l 2480.a 1.a $1$ $19.803$ \(\Q\) None 1240.2.a.b \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}-2q^{9}+2q^{11}+\cdots\)
2480.2.a.m 2480.a 1.a $1$ $19.803$ \(\Q\) None 155.2.a.a \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}-2q^{11}+\cdots\)
2480.2.a.n 2480.a 1.a $1$ $19.803$ \(\Q\) None 310.2.a.a \(0\) \(2\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+4q^{7}+q^{9}-4q^{13}+\cdots\)
2480.2.a.o 2480.a 1.a $1$ $19.803$ \(\Q\) None 620.2.a.a \(0\) \(3\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+2q^{7}+6q^{9}-2q^{11}+\cdots\)
2480.2.a.p 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{2}) \) None 1240.2.a.i \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-2q^{7}-q^{9}+(-2+\beta )q^{11}+\cdots\)
2480.2.a.q 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{6}) \) None 310.2.a.d \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+2q^{7}+3q^{9}+(-2+\beta )q^{11}+\cdots\)
2480.2.a.r 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{17}) \) None 1240.2.a.h \(0\) \(1\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(1+\beta )q^{9}+(2-2\beta )q^{11}+\cdots\)
2480.2.a.s 2480.a 1.a $2$ $19.803$ \(\Q(\sqrt{3}) \) None 310.2.a.c \(0\) \(2\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
2480.2.a.t 2480.a 1.a $3$ $19.803$ 3.3.756.1 None 620.2.a.d \(0\) \(-3\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+\beta _{2}q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
2480.2.a.u 2480.a 1.a $3$ $19.803$ 3.3.148.1 None 310.2.a.e \(0\) \(-2\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2480.2.a.v 2480.a 1.a $3$ $19.803$ 3.3.148.1 None 1240.2.a.j \(0\) \(3\) \(3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2480.2.a.w 2480.a 1.a $4$ $19.803$ 4.4.25492.1 None 620.2.a.e \(0\) \(-3\) \(4\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
2480.2.a.x 2480.a 1.a $4$ $19.803$ 4.4.8468.1 None 155.2.a.e \(0\) \(-1\) \(4\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
2480.2.a.y 2480.a 1.a $4$ $19.803$ 4.4.112820.1 None 1240.2.a.k \(0\) \(1\) \(-4\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}-\beta _{3})q^{7}+\cdots\)
2480.2.a.z 2480.a 1.a $4$ $19.803$ 4.4.20308.1 None 155.2.a.d \(0\) \(1\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}-q^{5}-\beta _{2}q^{7}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{9}+\cdots\)
2480.2.a.ba 2480.a 1.a $6$ $19.803$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 1240.2.a.m \(0\) \(1\) \(6\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(4-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
2480.2.a.bb 2480.a 1.a $6$ $19.803$ 6.6.473125168.1 None 1240.2.a.l \(0\) \(3\) \(-6\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2480))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2480)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(620))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1240))\)\(^{\oplus 2}\)