Properties

Label 1104.6.a
Level $1104$
Weight $6$
Character orbit 1104.a
Rep. character $\chi_{1104}(1,\cdot)$
Character field $\Q$
Dimension $110$
Newform subspaces $27$
Sturm bound $1152$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1104.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(1152\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1104))\).

Total New Old
Modular forms 972 110 862
Cusp forms 948 110 838
Eisenstein series 24 0 24

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.
\(+\)\(+\)\(+\)\(+\)\(13\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(12\)
\(-\)\(+\)\(+\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(+\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(51\)
Minus space\(-\)\(59\)

Trace form

\( 110 q - 18 q^{3} - 76 q^{5} + 124 q^{7} + 8910 q^{9} + O(q^{10}) \) \( 110 q - 18 q^{3} - 76 q^{5} + 124 q^{7} + 8910 q^{9} + 244 q^{13} - 404 q^{17} - 3236 q^{19} + 74594 q^{25} - 1458 q^{27} + 8564 q^{29} + 12616 q^{31} - 9432 q^{33} - 4776 q^{35} + 3764 q^{37} - 9468 q^{39} + 2476 q^{41} + 9900 q^{43} - 6156 q^{45} - 65256 q^{47} + 231086 q^{49} + 75268 q^{53} - 6624 q^{55} + 12888 q^{57} + 28960 q^{59} - 43452 q^{61} + 10044 q^{63} - 86904 q^{65} - 163532 q^{67} - 143840 q^{71} + 84316 q^{73} - 175374 q^{75} - 114736 q^{77} - 75740 q^{79} + 721710 q^{81} + 100968 q^{85} + 90828 q^{87} + 175580 q^{89} - 102440 q^{91} + 38424 q^{95} - 72804 q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1104))\) 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
1104.6.a.a $1$ $177.064$ \(\Q\) None \(0\) \(-9\) \(-46\) \(136\) $-$ $+$ $-$ \(q-9q^{3}-46q^{5}+136q^{7}+3^{4}q^{9}+\cdots\)
1104.6.a.b $1$ $177.064$ \(\Q\) None \(0\) \(9\) \(-82\) \(64\) $+$ $-$ $+$ \(q+9q^{3}-82q^{5}+2^{6}q^{7}+3^{4}q^{9}+412q^{11}+\cdots\)
1104.6.a.c $1$ $177.064$ \(\Q\) None \(0\) \(9\) \(-44\) \(70\) $-$ $-$ $+$ \(q+9q^{3}-44q^{5}+70q^{7}+3^{4}q^{9}+136q^{11}+\cdots\)
1104.6.a.d $1$ $177.064$ \(\Q\) None \(0\) \(9\) \(-10\) \(8\) $-$ $-$ $+$ \(q+9q^{3}-10q^{5}+8q^{7}+3^{4}q^{9}+300q^{11}+\cdots\)
1104.6.a.e $1$ $177.064$ \(\Q\) None \(0\) \(9\) \(76\) \(-210\) $-$ $-$ $+$ \(q+9q^{3}+76q^{5}-210q^{7}+3^{4}q^{9}+\cdots\)
1104.6.a.f $2$ $177.064$ \(\Q(\sqrt{154}) \) None \(0\) \(-18\) \(-4\) \(40\) $-$ $+$ $+$ \(q-9q^{3}+(-2+3\beta )q^{5}+(20+5\beta )q^{7}+\cdots\)
1104.6.a.g $2$ $177.064$ \(\Q(\sqrt{514}) \) None \(0\) \(18\) \(40\) \(100\) $-$ $-$ $-$ \(q+9q^{3}+(20+3\beta )q^{5}+(50-5\beta )q^{7}+\cdots\)
1104.6.a.h $2$ $177.064$ \(\Q(\sqrt{29}) \) None \(0\) \(18\) \(94\) \(118\) $-$ $-$ $+$ \(q+9q^{3}+(47-\beta )q^{5}+(59-11\beta )q^{7}+\cdots\)
1104.6.a.i $3$ $177.064$ 3.3.5333.1 None \(0\) \(-27\) \(-56\) \(114\) $-$ $+$ $+$ \(q-9q^{3}+(-21+4\beta _{1}+3\beta _{2})q^{5}+(33+\cdots)q^{7}+\cdots\)
1104.6.a.j $3$ $177.064$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-27\) \(-4\) \(34\) $-$ $+$ $-$ \(q-9q^{3}+(-1+\beta _{1})q^{5}+(11-\beta _{1}+\beta _{2})q^{7}+\cdots\)
1104.6.a.k $3$ $177.064$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(27\) \(-18\) \(50\) $-$ $-$ $-$ \(q+9q^{3}+(-6-\beta _{2})q^{5}+(17-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
1104.6.a.l $4$ $177.064$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-36\) \(-50\) \(62\) $-$ $+$ $-$ \(q-9q^{3}+(-13-\beta _{1}-\beta _{2})q^{5}+(15+\cdots)q^{7}+\cdots\)
1104.6.a.m $4$ $177.064$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-36\) \(54\) \(-348\) $-$ $+$ $+$ \(q-9q^{3}+(13-\beta _{1})q^{5}+(-87+\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.n $4$ $177.064$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(36\) \(-122\) \(-62\) $-$ $-$ $+$ \(q+9q^{3}+(-28+4\beta _{1}+\beta _{3})q^{5}+(-10+\cdots)q^{7}+\cdots\)
1104.6.a.o $4$ $177.064$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(36\) \(22\) \(62\) $-$ $-$ $-$ \(q+9q^{3}+(5+\beta _{1}+\beta _{2}-2\beta _{3})q^{5}+(18+\cdots)q^{7}+\cdots\)
1104.6.a.p $4$ $177.064$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(36\) \(22\) \(154\) $-$ $-$ $+$ \(q+9q^{3}+(6+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(39+\cdots)q^{7}+\cdots\)
1104.6.a.q $5$ $177.064$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-45\) \(16\) \(134\) $+$ $+$ $+$ \(q-9q^{3}+(3-\beta _{4})q^{5}+(3^{3}+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.r $5$ $177.064$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-45\) \(94\) \(-272\) $-$ $+$ $-$ \(q-9q^{3}+(19-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4})q^{5}+\cdots\)
1104.6.a.s $6$ $177.064$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-54\) \(50\) \(154\) $-$ $+$ $+$ \(q-9q^{3}+(8-\beta _{2})q^{5}+(26+\beta _{4})q^{7}+\cdots\)
1104.6.a.t $6$ $177.064$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(54\) \(-90\) \(-50\) $+$ $-$ $-$ \(q+9q^{3}+(-15+\beta _{5})q^{5}+(-8+\beta _{1}+\cdots)q^{7}+\cdots\)
1104.6.a.u $6$ $177.064$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(54\) \(-70\) \(-144\) $+$ $-$ $-$ \(q+9q^{3}+(-12+\beta _{1})q^{5}+(-24-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.v $6$ $177.064$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(54\) \(22\) \(-134\) $-$ $-$ $-$ \(q+9q^{3}+(4-\beta _{1})q^{5}+(-22-\beta _{4})q^{7}+\cdots\)
1104.6.a.w $6$ $177.064$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(54\) \(42\) \(82\) $+$ $-$ $+$ \(q+9q^{3}+(7+\beta _{2})q^{5}+(14-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.x $7$ $177.064$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-63\) \(-104\) \(182\) $+$ $+$ $-$ \(q-9q^{3}+(-15-\beta _{1})q^{5}+(26-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.y $7$ $177.064$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(63\) \(80\) \(-46\) $+$ $-$ $+$ \(q+9q^{3}+(11+\beta _{2})q^{5}+(-7-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.z $8$ $177.064$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-72\) \(-4\) \(-210\) $+$ $+$ $+$ \(q-9q^{3}+(-1+\beta _{1})q^{5}+(-26-\beta _{3}+\cdots)q^{7}+\cdots\)
1104.6.a.ba $8$ $177.064$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-72\) \(16\) \(36\) $+$ $+$ $-$ \(q-9q^{3}+(2+\beta _{1})q^{5}+(5+\beta _{2})q^{7}+3^{4}q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1104))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1104)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)