Properties

Label 4840.2.a
Level $4840$
Weight $2$
Character orbit 4840.a
Rep. character $\chi_{4840}(1,\cdot)$
Character field $\Q$
Dimension $109$
Newform subspaces $34$
Sturm bound $1584$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4840.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 34 \)
Sturm bound: \(1584\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4840))\).

Total New Old
Modular forms 840 109 731
Cusp forms 745 109 636
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.

\(2\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(12\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(17\)
\(+\)\(-\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(50\)
Minus space\(-\)\(59\)

Trace form

\( 109 q - 4 q^{3} + q^{5} - 4 q^{7} + 117 q^{9} + O(q^{10}) \) \( 109 q - 4 q^{3} + q^{5} - 4 q^{7} + 117 q^{9} - 6 q^{13} - 2 q^{17} - 12 q^{19} - 16 q^{21} - 4 q^{23} + 109 q^{25} - 16 q^{27} - 10 q^{29} - 24 q^{31} + 4 q^{35} - 10 q^{37} + 16 q^{39} + 18 q^{41} - 8 q^{43} - 3 q^{45} + 20 q^{47} + 105 q^{49} + 16 q^{51} + 14 q^{53} + 16 q^{57} + 12 q^{59} + 6 q^{61} - 20 q^{63} + 2 q^{65} - 4 q^{67} + 16 q^{69} - 16 q^{71} + 6 q^{73} - 4 q^{75} + 16 q^{79} + 101 q^{81} + 16 q^{83} - 2 q^{85} + 40 q^{87} + 18 q^{89} - 16 q^{91} + 4 q^{95} + 30 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4840))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 11
4840.2.a.a 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
4840.2.a.b 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
4840.2.a.c 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}+8q^{19}-8q^{23}+\cdots\)
4840.2.a.d 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}+4q^{13}+4q^{17}+\cdots\)
4840.2.a.e 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-3q^{9}-6q^{13}+6q^{17}+\cdots\)
4840.2.a.f 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{9}+2q^{13}-2q^{17}+\cdots\)
4840.2.a.g 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-3q^{7}-2q^{9}+4q^{13}+\cdots\)
4840.2.a.h 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(1\) \(-1\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+3q^{7}-2q^{9}-4q^{13}+\cdots\)
4840.2.a.i 4840.a 1.a $1$ $38.648$ \(\Q\) None \(0\) \(3\) \(1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+6q^{13}+\cdots\)
4840.2.a.j 4840.a 1.a $2$ $38.648$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-2q^{13}+\cdots\)
4840.2.a.k 4840.a 1.a $2$ $38.648$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(-2-\beta )q^{7}+2\beta q^{13}+\cdots\)
4840.2.a.l 4840.a 1.a $2$ $38.648$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(2+\beta )q^{7}-2\beta q^{13}+\cdots\)
4840.2.a.m 4840.a 1.a $2$ $38.648$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
4840.2.a.n 4840.a 1.a $2$ $38.648$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
4840.2.a.o 4840.a 1.a $2$ $38.648$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+2\beta q^{9}+\cdots\)
4840.2.a.p 4840.a 1.a $2$ $38.648$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(1+\beta )q^{7}+2\beta q^{9}+\cdots\)
4840.2.a.q 4840.a 1.a $3$ $38.648$ 3.3.568.1 None \(0\) \(-1\) \(3\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
4840.2.a.r 4840.a 1.a $3$ $38.648$ 3.3.568.1 None \(0\) \(-1\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
4840.2.a.s 4840.a 1.a $3$ $38.648$ 3.3.788.1 None \(0\) \(1\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
4840.2.a.t 4840.a 1.a $3$ $38.648$ 3.3.404.1 None \(0\) \(1\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
4840.2.a.u 4840.a 1.a $3$ $38.648$ 3.3.404.1 None \(0\) \(1\) \(-3\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
4840.2.a.v 4840.a 1.a $3$ $38.648$ 3.3.788.1 None \(0\) \(1\) \(-3\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
4840.2.a.w 4840.a 1.a $4$ $38.648$ 4.4.4752.1 None \(0\) \(-2\) \(-4\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(-2-\beta _{2}+\beta _{3})q^{7}+\cdots\)
4840.2.a.x 4840.a 1.a $4$ $38.648$ 4.4.4752.1 None \(0\) \(-2\) \(-4\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(2+\beta _{2}-\beta _{3})q^{7}+\cdots\)
4840.2.a.y 4840.a 1.a $4$ $38.648$ 4.4.725.1 None \(0\) \(-2\) \(4\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
4840.2.a.z 4840.a 1.a $4$ $38.648$ 4.4.725.1 None \(0\) \(-2\) \(4\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
4840.2.a.ba 4840.a 1.a $6$ $38.648$ 6.6.25903625.1 None \(0\) \(-3\) \(-6\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
4840.2.a.bb 4840.a 1.a $6$ $38.648$ 6.6.25903625.1 None \(0\) \(-3\) \(-6\) \(7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots\)
4840.2.a.bc 4840.a 1.a $6$ $38.648$ 6.6.22733568.1 None \(0\) \(-2\) \(6\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
4840.2.a.bd 4840.a 1.a $6$ $38.648$ 6.6.22733568.1 None \(0\) \(-2\) \(6\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(\beta _{3}+\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
4840.2.a.be 4840.a 1.a $6$ $38.648$ 6.6.45753625.1 None \(0\) \(2\) \(-6\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}-q^{5}+(-1+\beta _{2}+\beta _{5})q^{7}+\cdots\)
4840.2.a.bf 4840.a 1.a $6$ $38.648$ 6.6.45753625.1 None \(0\) \(2\) \(-6\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}-q^{5}+(1-\beta _{2}-\beta _{5})q^{7}+(-2\beta _{2}+\cdots)q^{9}+\cdots\)
4840.2.a.bg 4840.a 1.a $8$ $38.648$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(8\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)
4840.2.a.bh 4840.a 1.a $8$ $38.648$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(8\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4840)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\)\(^{\oplus 2}\)