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Properties

Label 2220.2.a
Level $2220$
Weight $2$
Character orbit 2220.a
Rep. character $\chi_{2220}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $11$
Sturm bound $912$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2220 = 2^{2} \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2220.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(912\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2220))\).

Total New Old
Modular forms 468 24 444
Cusp forms 445 24 421
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.

\(2\)\(3\)\(5\)\(37\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(+\)\(-\)$+$\(2\)
\(-\)\(+\)\(-\)\(+\)$+$\(3\)
\(-\)\(+\)\(-\)\(-\)$-$\(3\)
\(-\)\(-\)\(+\)\(+\)$+$\(3\)
\(-\)\(-\)\(+\)\(-\)$-$\(3\)
\(-\)\(-\)\(-\)\(+\)$-$\(4\)
\(-\)\(-\)\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(10\)
Minus space\(-\)\(14\)

Trace form

\( 24 q + 24 q^{9} + O(q^{10}) \) \( 24 q + 24 q^{9} + 8 q^{11} - 8 q^{17} - 8 q^{23} + 24 q^{25} - 16 q^{29} - 8 q^{31} - 4 q^{37} + 8 q^{41} - 16 q^{43} - 8 q^{47} + 24 q^{49} - 16 q^{51} + 8 q^{53} - 8 q^{57} + 8 q^{59} - 16 q^{61} + 8 q^{65} + 16 q^{67} + 8 q^{69} + 24 q^{71} + 8 q^{73} + 8 q^{77} + 24 q^{81} + 8 q^{83} + 8 q^{87} + 24 q^{89} - 8 q^{91} - 24 q^{93} + 16 q^{95} - 24 q^{97} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2220))\) 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 3 5 37
2220.2.a.a 2220.a 1.a $1$ $17.727$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+5q^{13}+\cdots\)
2220.2.a.b 2220.a 1.a $1$ $17.727$ \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2220.2.a.c 2220.a 1.a $1$ $17.727$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
2220.2.a.d 2220.a 1.a $2$ $17.727$ \(\Q(\sqrt{109}) \) None \(0\) \(-2\) \(-2\) \(-6\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-3q^{7}+q^{9}+\beta q^{11}-5q^{13}+\cdots\)
2220.2.a.e 2220.a 1.a $2$ $17.727$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}-\beta q^{11}+q^{13}+\cdots\)
2220.2.a.f 2220.a 1.a $2$ $17.727$ \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1-2\beta )q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
2220.2.a.g 2220.a 1.a $2$ $17.727$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-6\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}+(-1-3\beta )q^{11}+\cdots\)
2220.2.a.h 2220.a 1.a $3$ $17.727$ 3.3.1101.1 None \(0\) \(-3\) \(3\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
2220.2.a.i 2220.a 1.a $3$ $17.727$ 3.3.621.1 None \(0\) \(-3\) \(3\) \(6\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(2-\beta _{2})q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2220.2.a.j 2220.a 1.a $3$ $17.727$ 3.3.621.1 None \(0\) \(3\) \(-3\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta _{2}q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2220.2.a.k 2220.a 1.a $4$ $17.727$ 4.4.39605.1 None \(0\) \(4\) \(4\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1-\beta _{3})q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2220))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2220)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(740))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\)\(^{\oplus 2}\)