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Properties

Label 1104.2.a
Level $1104$
Weight $2$
Character orbit 1104.a
Rep. character $\chi_{1104}(1,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $15$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1104.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1104))\).

Total New Old
Modular forms 204 22 182
Cusp forms 181 22 159
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.

\(2\)\(3\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(15\)

Trace form

\( 22 q - 2 q^{3} + 4 q^{5} - 4 q^{7} + 22 q^{9} + O(q^{10}) \) \( 22 q - 2 q^{3} + 4 q^{5} - 4 q^{7} + 22 q^{9} + 4 q^{13} - 4 q^{17} - 4 q^{19} + 26 q^{25} - 2 q^{27} + 4 q^{29} + 8 q^{31} + 8 q^{33} + 24 q^{35} + 4 q^{37} + 4 q^{39} - 4 q^{41} + 12 q^{43} + 4 q^{45} + 24 q^{47} + 22 q^{49} + 20 q^{53} + 32 q^{55} - 8 q^{57} + 32 q^{59} + 20 q^{61} - 4 q^{63} - 24 q^{65} + 20 q^{67} + 32 q^{71} - 20 q^{73} + 2 q^{75} + 16 q^{77} - 28 q^{79} + 22 q^{81} + 8 q^{85} + 12 q^{87} - 20 q^{89} + 24 q^{91} + 24 q^{95} - 20 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\) 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 23
1104.2.a.a 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(-1\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
1104.2.a.b 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+2q^{13}-2q^{19}+\cdots\)
1104.2.a.c 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1104.2.a.d 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(1\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
1104.2.a.e 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(1\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
1104.2.a.f 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
1104.2.a.g 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1104.2.a.h 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(1\) \(2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
1104.2.a.i 1104.a 1.a $1$ $8.815$ \(\Q\) None \(0\) \(1\) \(4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
1104.2.a.j 1104.a 1.a $2$ $8.815$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots\)
1104.2.a.k 1104.a 1.a $2$ $8.815$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}-2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1104.2.a.l 1104.a 1.a $2$ $8.815$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+4\beta q^{11}+\cdots\)
1104.2.a.m 1104.a 1.a $2$ $8.815$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1104.2.a.n 1104.a 1.a $2$ $8.815$ \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+(-2+\beta )q^{7}+q^{9}+4q^{13}+\cdots\)
1104.2.a.o 1104.a 1.a $3$ $8.815$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1104)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)