Properties

Label 1100.2.a
Level $1100$
Weight $2$
Character orbit 1100.a
Rep. character $\chi_{1100}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $10$
Sturm bound $360$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(360\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1100))\).

Total New Old
Modular forms 198 17 181
Cusp forms 163 17 146
Eisenstein series 35 0 35

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
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(7\)
Minus space\(-\)\(10\)

Trace form

\( 17 q - q^{3} + 2 q^{7} + 24 q^{9} + O(q^{10}) \) \( 17 q - q^{3} + 2 q^{7} + 24 q^{9} + q^{11} + 8 q^{13} - 2 q^{17} + 12 q^{19} + 10 q^{21} + 3 q^{23} + 5 q^{27} - 16 q^{29} - 5 q^{31} - 3 q^{33} + 5 q^{37} - 24 q^{41} - 2 q^{43} - 16 q^{47} + 41 q^{49} - 6 q^{51} + 10 q^{53} - 8 q^{57} - 3 q^{59} + 16 q^{61} + 8 q^{63} + 9 q^{67} - q^{69} + 13 q^{71} + 24 q^{73} - 2 q^{77} - 22 q^{79} + 69 q^{81} - 18 q^{83} - 16 q^{87} - 11 q^{89} - 28 q^{91} + 11 q^{93} - 13 q^{97} + 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1100))\) 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
1100.2.a.a 1100.a 1.a $1$ $8.784$ \(\Q\) None 220.2.a.b \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+q^{11}+4q^{17}-4q^{19}+\cdots\)
1100.2.a.b 1100.a 1.a $1$ $8.784$ \(\Q\) None 44.2.a.a \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
1100.2.a.c 1100.a 1.a $1$ $8.784$ \(\Q\) None 220.2.b.a \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}-q^{11}+6q^{13}+2q^{17}+\cdots\)
1100.2.a.d 1100.a 1.a $1$ $8.784$ \(\Q\) None 220.2.b.a \(0\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-q^{11}-6q^{13}-2q^{17}+\cdots\)
1100.2.a.e 1100.a 1.a $1$ $8.784$ \(\Q\) None 220.2.a.a \(0\) \(2\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
1100.2.a.f 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{13}) \) None 1100.2.a.f \(0\) \(-3\) \(0\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
1100.2.a.g 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{21}) \) None 1100.2.a.g \(0\) \(-1\) \(0\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-3+\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots\)
1100.2.a.h 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{21}) \) None 1100.2.a.g \(0\) \(1\) \(0\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(3-\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots\)
1100.2.a.i 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{13}) \) None 1100.2.a.f \(0\) \(3\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
1100.2.a.j 1100.a 1.a $4$ $8.784$ \(\Q(\sqrt{3}, \sqrt{19})\) None 220.2.b.b \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(3+\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1100))\) into lower level spaces

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