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Properties

Label 1100.6.a
Level $1100$
Weight $6$
Character orbit 1100.a
Rep. character $\chi_{1100}(1,\cdot)$
Character field $\Q$
Dimension $79$
Newform subspaces $13$
Sturm bound $1080$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(1080\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1100))\).

Total New Old
Modular forms 918 79 839
Cusp forms 882 79 803
Eisenstein series 36 0 36

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
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(20\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(38\)
Minus space\(-\)\(41\)

Trace form

\( 79 q - q^{3} + 218 q^{7} + 5988 q^{9} + O(q^{10}) \) \( 79 q - q^{3} + 218 q^{7} + 5988 q^{9} + 121 q^{11} - 1016 q^{13} + 2234 q^{17} + 1340 q^{19} + 7478 q^{21} - 10297 q^{23} + 9125 q^{27} + 360 q^{29} - 2433 q^{31} - 5929 q^{33} + 23971 q^{37} - 42240 q^{39} + 55408 q^{41} + 1470 q^{43} + 20040 q^{47} + 226503 q^{49} + 26042 q^{51} + 20326 q^{53} + 11592 q^{57} - 5307 q^{59} - 24856 q^{61} + 106184 q^{63} + 32561 q^{67} + 298233 q^{69} - 11535 q^{71} + 102104 q^{73} - 38478 q^{77} - 73102 q^{79} + 343851 q^{81} + 55374 q^{83} + 104640 q^{87} - 17513 q^{89} + 68868 q^{91} + 121405 q^{93} - 134143 q^{97} - 143022 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1100))\) 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
1100.6.a.a 1100.a 1.a $1$ $176.422$ \(\Q\) None 44.6.a.a \(0\) \(-7\) \(0\) \(50\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-7q^{3}+50q^{7}-194q^{9}+11^{2}q^{11}+\cdots\)
1100.6.a.b 1100.a 1.a $2$ $176.422$ \(\Q(\sqrt{31}) \) None 44.6.a.b \(0\) \(6\) \(0\) \(-268\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{3}+(-134-3\beta )q^{7}+(262+\cdots)q^{9}+\cdots\)
1100.6.a.c 1100.a 1.a $2$ $176.422$ \(\Q(\sqrt{1761}) \) None 220.6.a.a \(0\) \(19\) \(0\) \(131\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(10-\beta )q^{3}+(68-5\beta )q^{7}+(297-19\beta )q^{9}+\cdots\)
1100.6.a.d 1100.a 1.a $3$ $176.422$ 3.3.399324.1 None 220.6.a.b \(0\) \(-1\) \(0\) \(155\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(50-7\beta _{1}+2\beta _{2})q^{7}+(-6^{2}+\cdots)q^{9}+\cdots\)
1100.6.a.e 1100.a 1.a $4$ $176.422$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 220.6.a.d \(0\) \(0\) \(0\) \(30\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(8-2\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots\)
1100.6.a.f 1100.a 1.a $4$ $176.422$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 220.6.a.c \(0\) \(0\) \(0\) \(250\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(63+\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
1100.6.a.g 1100.a 1.a $5$ $176.422$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 220.6.a.e \(0\) \(-18\) \(0\) \(-130\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-4+\beta _{1})q^{3}+(-26+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1100.6.a.h 1100.a 1.a $8$ $176.422$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1100.6.a.h \(0\) \(-27\) \(0\) \(-95\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1})q^{3}+(-12-\beta _{3})q^{7}+(45+\cdots)q^{9}+\cdots\)
1100.6.a.i 1100.a 1.a $8$ $176.422$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1100.6.a.i \(0\) \(-9\) \(0\) \(-175\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(-22-2\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
1100.6.a.j 1100.a 1.a $8$ $176.422$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1100.6.a.i \(0\) \(9\) \(0\) \(175\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(22+2\beta _{1}-\beta _{5})q^{7}+\cdots\)
1100.6.a.k 1100.a 1.a $8$ $176.422$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1100.6.a.h \(0\) \(27\) \(0\) \(95\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{3}+(12+\beta _{3})q^{7}+(45+6\beta _{1}+\cdots)q^{9}+\cdots\)
1100.6.a.l 1100.a 1.a $12$ $176.422$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 220.6.b.a \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{9}q^{7}+(134+\beta _{2})q^{9}-11^{2}q^{11}+\cdots\)
1100.6.a.m 1100.a 1.a $14$ $176.422$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 220.6.b.b \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{8})q^{7}+(82+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1100))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1100)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 2}\)