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Properties

Label 2420.2.a
Level $2420$
Weight $2$
Character orbit 2420.a
Rep. character $\chi_{2420}(1,\cdot)$
Character field $\Q$
Dimension $37$
Newform subspaces $15$
Sturm bound $792$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2420 = 2^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2420.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(792\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2420))\).

Total New Old
Modular forms 432 37 395
Cusp forms 361 37 324
Eisenstein series 71 0 71

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
\(-\)\(+\)\(+\)$-$\(12\)
\(-\)\(+\)\(-\)$+$\(7\)
\(-\)\(-\)\(+\)$+$\(6\)
\(-\)\(-\)\(-\)$-$\(12\)
Plus space\(+\)\(13\)
Minus space\(-\)\(24\)

Trace form

\( 37 q + 2 q^{3} - q^{5} + 2 q^{7} + 37 q^{9} + O(q^{10}) \) \( 37 q + 2 q^{3} - q^{5} + 2 q^{7} + 37 q^{9} + 2 q^{13} - 2 q^{15} + 10 q^{17} + 12 q^{19} - 4 q^{21} - 2 q^{23} + 37 q^{25} - 4 q^{27} - 2 q^{29} + 6 q^{35} + 10 q^{37} - 4 q^{39} - 2 q^{41} - 2 q^{43} - q^{45} - 10 q^{47} + 45 q^{49} - 4 q^{51} + 6 q^{53} - 8 q^{57} + 10 q^{61} + 2 q^{63} + 6 q^{65} + 2 q^{67} - 4 q^{69} + 24 q^{71} + 18 q^{73} + 2 q^{75} - 8 q^{79} + 89 q^{81} - 18 q^{83} - 2 q^{85} - 4 q^{87} - 6 q^{89} + 52 q^{91} + 96 q^{93} + 4 q^{95} + 62 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\) 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
2420.2.a.a 2420.a 1.a $1$ $19.324$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots\)
2420.2.a.b 2420.a 1.a $1$ $19.324$ \(\Q\) None \(0\) \(-2\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+4q^{7}+q^{9}+4q^{13}+\cdots\)
2420.2.a.c 2420.a 1.a $1$ $19.324$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-3q^{9}-4q^{13}+4q^{17}+\cdots\)
2420.2.a.d 2420.a 1.a $1$ $19.324$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-3q^{9}+4q^{13}-4q^{17}+\cdots\)
2420.2.a.e 2420.a 1.a $1$ $19.324$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}-2q^{9}+2q^{13}-q^{15}+\cdots\)
2420.2.a.f 2420.a 1.a $1$ $19.324$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}-2q^{13}-q^{15}+\cdots\)
2420.2.a.g 2420.a 1.a $1$ $19.324$ \(\Q\) None \(0\) \(2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}+2q^{15}+4q^{17}+\cdots\)
2420.2.a.h 2420.a 1.a $2$ $19.324$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta q^{7}-2q^{9}-q^{15}-4\beta q^{19}+\cdots\)
2420.2.a.i 2420.a 1.a $3$ $19.324$ 3.3.1524.1 None \(0\) \(1\) \(3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
2420.2.a.j 2420.a 1.a $3$ $19.324$ 3.3.1524.1 None \(0\) \(1\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
2420.2.a.k 2420.a 1.a $4$ $19.324$ 4.4.2525.1 None \(0\) \(0\) \(4\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
2420.2.a.l 2420.a 1.a $4$ $19.324$ 4.4.2525.1 None \(0\) \(0\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2420.2.a.m 2420.a 1.a $4$ $19.324$ 4.4.5125.1 None \(0\) \(2\) \(-4\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
2420.2.a.n 2420.a 1.a $4$ $19.324$ 4.4.5125.1 None \(0\) \(2\) \(-4\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
2420.2.a.o 2420.a 1.a $6$ $19.324$ 6.6.507624192.1 None \(0\) \(-2\) \(-6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(3-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2420))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2420)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 2}\)