↑

Properties

Label 1100.4.a
Level $1100$
Weight $4$
Character orbit 1100.a
Rep. character $\chi_{1100}(1,\cdot)$
Character field $\Q$
Dimension $47$
Newform subspaces $15$
Sturm bound $720$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(720\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1100))\).

Total New Old
Modular forms 558 47 511
Cusp forms 522 47 475
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
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(11\)
Plus space\(+\)\(25\)
Minus space\(-\)\(22\)

Trace form

\( 47 q + 8 q^{3} - 16 q^{7} + 417 q^{9} + O(q^{10}) \) \( 47 q + 8 q^{3} - 16 q^{7} + 417 q^{9} - 11 q^{11} + 106 q^{13} + 50 q^{17} - 156 q^{19} - 4 q^{21} + 176 q^{23} - 64 q^{27} + 462 q^{29} + 392 q^{31} - 22 q^{33} + 124 q^{37} + 1296 q^{39} + 370 q^{41} - 76 q^{43} + 612 q^{47} + 2447 q^{49} + 584 q^{51} - 638 q^{53} - 528 q^{57} + 36 q^{59} - 530 q^{61} + 344 q^{63} - 1416 q^{67} - 534 q^{69} - 2544 q^{71} + 270 q^{73} + 396 q^{77} + 2048 q^{79} + 2343 q^{81} + 1644 q^{83} - 4176 q^{87} - 2864 q^{89} + 2440 q^{91} - 1094 q^{93} + 1592 q^{97} + 33 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1100))\) 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
1100.4.a.a 1100.a 1.a $1$ $64.902$ \(\Q\) None 220.4.a.c \(0\) \(-8\) \(0\) \(-24\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{3}-24q^{7}+37q^{9}-11q^{11}+\cdots\)
1100.4.a.b 1100.a 1.a $1$ $64.902$ \(\Q\) None 220.4.a.b \(0\) \(-5\) \(0\) \(19\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}+19q^{7}-2q^{9}-11q^{11}+62q^{13}+\cdots\)
1100.4.a.c 1100.a 1.a $1$ $64.902$ \(\Q\) None 220.4.a.a \(0\) \(5\) \(0\) \(-11\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+5q^{3}-11q^{7}-2q^{9}-11q^{11}+22q^{13}+\cdots\)
1100.4.a.d 1100.a 1.a $1$ $64.902$ \(\Q\) None 44.4.a.a \(0\) \(5\) \(0\) \(26\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+5q^{3}+26q^{7}-2q^{9}-11q^{11}-52q^{13}+\cdots\)
1100.4.a.e 1100.a 1.a $2$ $64.902$ \(\Q(\sqrt{97}) \) None 44.4.a.b \(0\) \(-9\) \(0\) \(-10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-4-\beta )q^{3}+(-8+6\beta )q^{7}+(13+\cdots)q^{9}+\cdots\)
1100.4.a.f 1100.a 1.a $2$ $64.902$ \(\Q(\sqrt{19}) \) None 220.4.b.a \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{7}-8q^{9}-11q^{11}+2^{4}\beta q^{13}+\cdots\)
1100.4.a.g 1100.a 1.a $2$ $64.902$ \(\Q(\sqrt{6}) \) None 220.4.a.e \(0\) \(8\) \(0\) \(-36\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(4+\beta )q^{3}+(-18-2\beta )q^{7}+(13+8\beta )q^{9}+\cdots\)
1100.4.a.h 1100.a 1.a $2$ $64.902$ \(\Q(\sqrt{97}) \) None 220.4.a.d \(0\) \(9\) \(0\) \(15\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(5-\beta )q^{3}+(7+\beta )q^{7}+(22-9\beta )q^{9}+\cdots\)
1100.4.a.i 1100.a 1.a $3$ $64.902$ 3.3.9192.1 None 220.4.a.f \(0\) \(3\) \(0\) \(5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(2+\beta _{1}-2\beta _{2})q^{7}+(9+\cdots)q^{9}+\cdots\)
1100.4.a.j 1100.a 1.a $5$ $64.902$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1100.4.a.j \(0\) \(-6\) \(0\) \(-50\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(-10-\beta _{1}-\beta _{4})q^{7}+\cdots\)
1100.4.a.k 1100.a 1.a $5$ $64.902$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1100.4.a.k \(0\) \(-6\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+\beta _{2}q^{7}+(11+2\beta _{1}+\cdots)q^{9}+\cdots\)
1100.4.a.l 1100.a 1.a $5$ $64.902$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1100.4.a.k \(0\) \(6\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}-\beta _{2}q^{7}+(11+2\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
1100.4.a.m 1100.a 1.a $5$ $64.902$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 1100.4.a.j \(0\) \(6\) \(0\) \(50\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(10+\beta _{1}+\beta _{4})q^{7}+(11+\cdots)q^{9}+\cdots\)
1100.4.a.n 1100.a 1.a $6$ $64.902$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 220.4.b.c \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-2\beta _{1}-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1100.4.a.o 1100.a 1.a $6$ $64.902$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 220.4.b.b \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{5}q^{7}+(8-\beta _{2}-\beta _{4})q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1100))\) into lower level spaces

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