Properties

Label 2200.2.a
Level $2200$
Weight $2$
Character orbit 2200.a
Rep. character $\chi_{2200}(1,\cdot)$
Character field $\Q$
Dimension $47$
Newform subspaces $25$
Sturm bound $720$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2200.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2200))\).

Total New Old
Modular forms 384 47 337
Cusp forms 337 47 290
Eisenstein series 47 0 47

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
\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)$+$\(7\)
\(-\)\(+\)\(+\)$-$\(7\)
\(-\)\(+\)\(-\)$+$\(4\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(8\)
Plus space\(+\)\(21\)
Minus space\(-\)\(26\)

Trace form

\( 47 q - 2 q^{3} - 4 q^{7} + 41 q^{9} + O(q^{10}) \) \( 47 q - 2 q^{3} - 4 q^{7} + 41 q^{9} + 3 q^{11} - 6 q^{13} + 2 q^{17} - 4 q^{19} + 4 q^{21} - 6 q^{23} - 14 q^{27} + 30 q^{29} - 14 q^{31} + 2 q^{33} + 16 q^{37} + 18 q^{41} - 16 q^{43} + 20 q^{47} + 31 q^{49} - 4 q^{51} + 10 q^{53} + 32 q^{57} + 14 q^{59} + 14 q^{61} + 24 q^{63} - 6 q^{67} + 22 q^{69} - 18 q^{71} - 18 q^{73} + 4 q^{77} - 52 q^{79} + 71 q^{81} - 8 q^{83} + 24 q^{89} - 48 q^{91} - 10 q^{93} - 8 q^{97} + 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2200))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 11
2200.2.a.a 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.a.d \(0\) \(-3\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{7}+6q^{9}-q^{11}+6q^{13}+\cdots\)
2200.2.a.b 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.b.b \(0\) \(-2\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
2200.2.a.c 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.b.a \(0\) \(-2\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}-q^{11}-4q^{17}+\cdots\)
2200.2.a.d 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.b.c \(0\) \(-1\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-q^{11}+q^{17}+q^{19}+\cdots\)
2200.2.a.e 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.a.c \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{7}-3q^{9}-q^{11}-6q^{13}+6q^{17}+\cdots\)
2200.2.a.f 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.a.a \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-q^{11}-8q^{19}+8q^{23}+\cdots\)
2200.2.a.g 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.a.b \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}+q^{11}+4q^{13}+4q^{17}+\cdots\)
2200.2.a.h 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.b.c \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
2200.2.a.i 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.b.a \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-q^{11}+4q^{17}+\cdots\)
2200.2.a.j 2200.a 1.a $1$ $17.567$ \(\Q\) None 440.2.b.b \(0\) \(2\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
2200.2.a.k 2200.a 1.a $1$ $17.567$ \(\Q\) None 88.2.a.a \(0\) \(3\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}-q^{11}+6q^{17}+\cdots\)
2200.2.a.l 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None 440.2.a.g \(0\) \(-1\) \(0\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2-\beta )q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
2200.2.a.m 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None 440.2.a.f \(0\) \(-1\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
2200.2.a.n 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None 2200.2.a.n \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}-q^{11}+\cdots\)
2200.2.a.o 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None 88.2.a.b \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2\beta q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
2200.2.a.p 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None 2200.2.a.p \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{7}+(-2+\beta )q^{9}+q^{11}+\cdots\)
2200.2.a.q 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None 2200.2.a.p \(0\) \(1\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2200.2.a.r 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{5}) \) None 2200.2.a.n \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2200.2.a.s 2200.a 1.a $2$ $17.567$ \(\Q(\sqrt{17}) \) None 440.2.a.e \(0\) \(1\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{7}+(1+\beta )q^{9}+q^{11}-2q^{13}+\cdots\)
2200.2.a.t 2200.a 1.a $3$ $17.567$ 3.3.837.1 None 2200.2.a.t \(0\) \(-3\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
2200.2.a.u 2200.a 1.a $3$ $17.567$ 3.3.1229.1 None 2200.2.a.u \(0\) \(-1\) \(0\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
2200.2.a.v 2200.a 1.a $3$ $17.567$ 3.3.1229.1 None 2200.2.a.u \(0\) \(1\) \(0\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
2200.2.a.w 2200.a 1.a $3$ $17.567$ 3.3.837.1 None 2200.2.a.t \(0\) \(3\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
2200.2.a.x 2200.a 1.a $4$ $17.567$ 4.4.54764.1 None 440.2.b.d \(0\) \(-1\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots\)
2200.2.a.y 2200.a 1.a $4$ $17.567$ 4.4.54764.1 None 440.2.b.d \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2200)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1100))\)\(^{\oplus 2}\)