Properties

Label 7220.2.a
Level $7220$
Weight $2$
Character orbit 7220.a
Rep. character $\chi_{7220}(1,\cdot)$
Character field $\Q$
Dimension $113$
Newform subspaces $26$
Sturm bound $2280$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7220.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(2280\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7220))\).

Total New Old
Modular forms 1200 113 1087
Cusp forms 1081 113 968
Eisenstein series 119 0 119

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

\(2\)\(5\)\(19\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(33\)
\(-\)\(+\)\(-\)\(+\)\(24\)
\(-\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(-\)\(-\)\(-\)\(33\)
Plus space\(+\)\(47\)
Minus space\(-\)\(66\)

Trace form

\( 113 q + 2 q^{3} - q^{5} - 2 q^{7} + 113 q^{9} + O(q^{10}) \) \( 113 q + 2 q^{3} - q^{5} - 2 q^{7} + 113 q^{9} + 8 q^{11} + 2 q^{13} + 2 q^{15} + 2 q^{17} - 4 q^{21} + 10 q^{23} + 113 q^{25} + 8 q^{27} - 2 q^{29} + 12 q^{31} + 4 q^{33} + 2 q^{35} + 6 q^{37} - 8 q^{39} + 14 q^{41} + 2 q^{43} - 9 q^{45} + 10 q^{47} + 125 q^{49} - 4 q^{51} + 6 q^{53} - 12 q^{59} + 10 q^{61} - 22 q^{63} + 10 q^{65} - 6 q^{67} + 4 q^{69} - 4 q^{71} + 18 q^{73} + 2 q^{75} - 16 q^{77} + 8 q^{79} + 77 q^{81} - 22 q^{83} + 6 q^{85} - 8 q^{87} + 10 q^{89} - 4 q^{91} - 32 q^{93} + 14 q^{97} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7220))\) 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 19
7220.2.a.a 7220.a 1.a $1$ $57.652$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+\cdots\)
7220.2.a.b 7220.a 1.a $1$ $57.652$ \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
7220.2.a.c 7220.a 1.a $1$ $57.652$ \(\Q\) None \(0\) \(-2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
7220.2.a.d 7220.a 1.a $1$ $57.652$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
7220.2.a.e 7220.a 1.a $1$ $57.652$ \(\Q\) None \(0\) \(2\) \(-1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+\cdots\)
7220.2.a.f 7220.a 1.a $1$ $57.652$ \(\Q\) None \(0\) \(2\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
7220.2.a.g 7220.a 1.a $1$ $57.652$ \(\Q\) None \(0\) \(2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
7220.2.a.h 7220.a 1.a $2$ $57.652$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+2q^{7}+(1-2\beta )q^{9}+\cdots\)
7220.2.a.i 7220.a 1.a $2$ $57.652$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}-3q^{7}+(-2+\beta )q^{9}+\cdots\)
7220.2.a.j 7220.a 1.a $2$ $57.652$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{3}-q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots\)
7220.2.a.k 7220.a 1.a $2$ $57.652$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{3}-q^{5}+\beta q^{7}+2q^{9}+(-2+\cdots)q^{11}+\cdots\)
7220.2.a.l 7220.a 1.a $2$ $57.652$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-3q^{7}+(-2+\beta )q^{9}+\cdots\)
7220.2.a.m 7220.a 1.a $2$ $57.652$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+q^{5}+(-2+2\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
7220.2.a.n 7220.a 1.a $3$ $57.652$ 3.3.257.1 None \(0\) \(-1\) \(-3\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}+(1+\beta _{2})q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.o 7220.a 1.a $3$ $57.652$ 3.3.257.1 None \(0\) \(1\) \(-3\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-q^{5}+(1+\beta _{2})q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.p 7220.a 1.a $4$ $57.652$ 4.4.133593.1 None \(0\) \(-1\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7220.2.a.q 7220.a 1.a $4$ $57.652$ 4.4.7168.1 None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}-\beta _{3}q^{7}+(3+\beta _{3})q^{9}+\cdots\)
7220.2.a.r 7220.a 1.a $4$ $57.652$ 4.4.133593.1 None \(0\) \(1\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7220.2.a.s 7220.a 1.a $8$ $57.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(8\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{6})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.t 7220.a 1.a $8$ $57.652$ 8.8.\(\cdots\).2 None \(0\) \(0\) \(8\) \(-10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
7220.2.a.u 7220.a 1.a $8$ $57.652$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(8\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{6})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.v 7220.a 1.a $9$ $57.652$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(-9\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
7220.2.a.w 7220.a 1.a $9$ $57.652$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(9\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-\beta _{2}-\beta _{5}+\beta _{8})q^{7}+\cdots\)
7220.2.a.x 7220.a 1.a $9$ $57.652$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(-9\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
7220.2.a.y 7220.a 1.a $9$ $57.652$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(9\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-\beta _{2}-\beta _{5}+\beta _{8})q^{7}+\cdots\)
7220.2.a.z 7220.a 1.a $16$ $57.652$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-16\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2})q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7220))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7220)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3610))\)\(^{\oplus 2}\)