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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7220))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 19
7220.2.a.a \(1\) \(57.652\) \(\Q\) None \(0\) \(-2\) \(-1\) \(-4\) \(-\) \(+\) \(-\) \(q-2q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+\cdots\)
7220.2.a.b \(1\) \(57.652\) \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q-2q^{3}-q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
7220.2.a.c \(1\) \(57.652\) \(\Q\) None \(0\) \(-2\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
7220.2.a.d \(1\) \(57.652\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
7220.2.a.e \(1\) \(57.652\) \(\Q\) None \(0\) \(2\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(q+2q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+\cdots\)
7220.2.a.f \(1\) \(57.652\) \(\Q\) None \(0\) \(2\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q+2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
7220.2.a.g \(1\) \(57.652\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
7220.2.a.h \(2\) \(57.652\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+(-1+\beta )q^{3}+q^{5}+2q^{7}+(1-2\beta )q^{9}+\cdots\)
7220.2.a.i \(2\) \(57.652\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(-6\) \(-\) \(+\) \(-\) \(q-\beta q^{3}-q^{5}-3q^{7}+(-2+\beta )q^{9}+\cdots\)
7220.2.a.j \(2\) \(57.652\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(q+(1-2\beta )q^{3}-q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots\)
7220.2.a.k \(2\) \(57.652\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(q+(1-2\beta )q^{3}-q^{5}+\beta q^{7}+2q^{9}+(-2+\cdots)q^{11}+\cdots\)
7220.2.a.l \(2\) \(57.652\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(-6\) \(-\) \(+\) \(-\) \(q+\beta q^{3}-q^{5}-3q^{7}+(-2+\beta )q^{9}+\cdots\)
7220.2.a.m \(2\) \(57.652\) \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(q+(2+\beta )q^{3}+q^{5}+(-2+2\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
7220.2.a.n \(3\) \(57.652\) 3.3.257.1 None \(0\) \(-1\) \(-3\) \(2\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{3}-q^{5}+(1+\beta _{2})q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.o \(3\) \(57.652\) 3.3.257.1 None \(0\) \(1\) \(-3\) \(2\) \(-\) \(+\) \(-\) \(q-\beta _{2}q^{3}-q^{5}+(1+\beta _{2})q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.p \(4\) \(57.652\) 4.4.133593.1 None \(0\) \(-1\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7220.2.a.q \(4\) \(57.652\) 4.4.7168.1 None \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}-q^{5}-\beta _{3}q^{7}+(3+\beta _{3})q^{9}+\cdots\)
7220.2.a.r \(4\) \(57.652\) 4.4.133593.1 None \(0\) \(1\) \(4\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7220.2.a.s \(8\) \(57.652\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(8\) \(5\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{6})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.t \(8\) \(57.652\) 8.8.\(\cdots\).2 None \(0\) \(0\) \(8\) \(-10\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}+(-1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
7220.2.a.u \(8\) \(57.652\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(8\) \(5\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{6})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7220.2.a.v \(9\) \(57.652\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(-9\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
7220.2.a.w \(9\) \(57.652\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(9\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}+q^{5}+(-\beta _{2}-\beta _{5}+\beta _{8})q^{7}+\cdots\)
7220.2.a.x \(9\) \(57.652\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(-9\) \(0\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{4}+\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
7220.2.a.y \(9\) \(57.652\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(9\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+q^{5}+(-\beta _{2}-\beta _{5}+\beta _{8})q^{7}+\cdots\)
7220.2.a.z \(16\) \(57.652\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-16\) \(10\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2})q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)

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

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