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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 23
1104.2.a.a \(1\) \(8.815\) \(\Q\) None \(0\) \(-1\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
1104.2.a.b \(1\) \(8.815\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{7}+q^{9}+2q^{13}-2q^{19}+\cdots\)
1104.2.a.c \(1\) \(8.815\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1104.2.a.d \(1\) \(8.815\) \(\Q\) None \(0\) \(1\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
1104.2.a.e \(1\) \(8.815\) \(\Q\) None \(0\) \(1\) \(-2\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
1104.2.a.f \(1\) \(8.815\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
1104.2.a.g \(1\) \(8.815\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1104.2.a.h \(1\) \(8.815\) \(\Q\) None \(0\) \(1\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
1104.2.a.i \(1\) \(8.815\) \(\Q\) None \(0\) \(1\) \(4\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
1104.2.a.j \(2\) \(8.815\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+(-1-\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots\)
1104.2.a.k \(2\) \(8.815\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-4\) \(+\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{5}-2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1104.2.a.l \(2\) \(8.815\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+4\beta q^{11}+\cdots\)
1104.2.a.m \(2\) \(8.815\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1104.2.a.n \(2\) \(8.815\) \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+(-2+\beta )q^{7}+q^{9}+4q^{13}+\cdots\)
1104.2.a.o \(3\) \(8.815\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)

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

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