Properties

Label 5824.2.a
Level $5824$
Weight $2$
Character orbit 5824.a
Rep. character $\chi_{5824}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $66$
Sturm bound $1792$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5824 = 2^{6} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5824.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 66 \)
Sturm bound: \(1792\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5824))\).

Total New Old
Modular forms 920 144 776
Cusp forms 873 144 729
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(20\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(16\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(16\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(20\)
Plus space\(+\)\(66\)
Minus space\(-\)\(78\)

Trace form

\( 144 q + 144 q^{9} + O(q^{10}) \) \( 144 q + 144 q^{9} + 144 q^{25} + 16 q^{29} + 32 q^{33} + 16 q^{37} + 32 q^{41} - 96 q^{45} + 144 q^{49} - 80 q^{53} + 32 q^{57} + 64 q^{61} - 32 q^{69} + 16 q^{77} + 176 q^{81} + 64 q^{85} - 96 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5824))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 13
5824.2.a.a $1$ $46.505$ \(\Q\) None \(0\) \(-3\) \(0\) \(1\) $+$ $-$ $-$ \(q-3q^{3}+q^{7}+6q^{9}+5q^{11}+q^{13}+\cdots\)
5824.2.a.b $1$ $46.505$ \(\Q\) None \(0\) \(-3\) \(4\) \(-1\) $+$ $+$ $-$ \(q-3q^{3}+4q^{5}-q^{7}+6q^{9}-q^{11}+\cdots\)
5824.2.a.c $1$ $46.505$ \(\Q\) None \(0\) \(-2\) \(-3\) \(1\) $+$ $-$ $-$ \(q-2q^{3}-3q^{5}+q^{7}+q^{9}+q^{13}+6q^{15}+\cdots\)
5824.2.a.d $1$ $46.505$ \(\Q\) None \(0\) \(-2\) \(-1\) \(1\) $-$ $-$ $+$ \(q-2q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
5824.2.a.e $1$ $46.505$ \(\Q\) None \(0\) \(-2\) \(1\) \(-1\) $-$ $+$ $-$ \(q-2q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
5824.2.a.f $1$ $46.505$ \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) $-$ $+$ $+$ \(q-2q^{3}+3q^{5}-q^{7}+q^{9}-q^{13}-6q^{15}+\cdots\)
5824.2.a.g $1$ $46.505$ \(\Q\) None \(0\) \(-1\) \(-4\) \(-1\) $+$ $+$ $+$ \(q-q^{3}-4q^{5}-q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
5824.2.a.h $1$ $46.505$ \(\Q\) None \(0\) \(-1\) \(-4\) \(1\) $-$ $-$ $+$ \(q-q^{3}-4q^{5}+q^{7}-2q^{9}-5q^{11}+\cdots\)
5824.2.a.i $1$ $46.505$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ \(q-q^{3}-q^{7}-2q^{9}+q^{11}-q^{13}+4q^{17}+\cdots\)
5824.2.a.j $1$ $46.505$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $-$ \(q-q^{3}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
5824.2.a.k $1$ $46.505$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $-$ $+$ \(q-q^{3}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
5824.2.a.l $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $-$ \(q-2q^{5}-q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots\)
5824.2.a.m $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $-$ \(q-2q^{5}+q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots\)
5824.2.a.n $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $+$ \(q+q^{5}-q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots\)
5824.2.a.o $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $+$ \(q+q^{5}+q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
5824.2.a.p $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $+$ \(q+2q^{5}-q^{7}-3q^{9}+4q^{11}-q^{13}+\cdots\)
5824.2.a.q $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $-$ $+$ \(q+2q^{5}+q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
5824.2.a.r $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(3\) \(-1\) $-$ $+$ $-$ \(q+3q^{5}-q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
5824.2.a.s $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(3\) \(-1\) $+$ $+$ $-$ \(q+3q^{5}-q^{7}-3q^{9}+6q^{11}+q^{13}+\cdots\)
5824.2.a.t $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $-$ \(q+3q^{5}+q^{7}-3q^{9}-6q^{11}+q^{13}+\cdots\)
5824.2.a.u $1$ $46.505$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $+$ $-$ $-$ \(q+3q^{5}+q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
5824.2.a.v $1$ $46.505$ \(\Q\) None \(0\) \(1\) \(-4\) \(-1\) $-$ $+$ $+$ \(q+q^{3}-4q^{5}-q^{7}-2q^{9}+5q^{11}+\cdots\)
5824.2.a.w $1$ $46.505$ \(\Q\) None \(0\) \(1\) \(-4\) \(1\) $-$ $-$ $+$ \(q+q^{3}-4q^{5}+q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
5824.2.a.x $1$ $46.505$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ \(q+q^{3}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
5824.2.a.y $1$ $46.505$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $+$ $-$ $-$ \(q+q^{3}+q^{7}-2q^{9}-3q^{11}+q^{13}+\cdots\)
5824.2.a.z $1$ $46.505$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $+$ \(q+q^{3}+q^{7}-2q^{9}-q^{11}-q^{13}+4q^{17}+\cdots\)
5824.2.a.ba $1$ $46.505$ \(\Q\) None \(0\) \(2\) \(-3\) \(-1\) $-$ $+$ $-$ \(q+2q^{3}-3q^{5}-q^{7}+q^{9}+q^{13}-6q^{15}+\cdots\)
5824.2.a.bb $1$ $46.505$ \(\Q\) None \(0\) \(2\) \(-1\) \(-1\) $+$ $+$ $+$ \(q+2q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
5824.2.a.bc $1$ $46.505$ \(\Q\) None \(0\) \(2\) \(1\) \(1\) $+$ $-$ $-$ \(q+2q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
5824.2.a.bd $1$ $46.505$ \(\Q\) None \(0\) \(2\) \(3\) \(1\) $+$ $-$ $+$ \(q+2q^{3}+3q^{5}+q^{7}+q^{9}-q^{13}+6q^{15}+\cdots\)
5824.2.a.be $1$ $46.505$ \(\Q\) None \(0\) \(3\) \(0\) \(-1\) $-$ $+$ $-$ \(q+3q^{3}-q^{7}+6q^{9}-5q^{11}+q^{13}+\cdots\)
5824.2.a.bf $1$ $46.505$ \(\Q\) None \(0\) \(3\) \(4\) \(1\) $-$ $-$ $-$ \(q+3q^{3}+4q^{5}+q^{7}+6q^{9}+q^{11}+\cdots\)
5824.2.a.bg $2$ $46.505$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(2\) \(-2\) $-$ $+$ $+$ \(q+(-2+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
5824.2.a.bh $2$ $46.505$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $-$ $+$ \(q+(-1+\beta )q^{3}-\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
5824.2.a.bi $2$ $46.505$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $-$ $-$ \(q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
5824.2.a.bj $2$ $46.505$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(1\) \(-2\) $+$ $+$ $+$ \(q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
5824.2.a.bk $2$ $46.505$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(-2\) $-$ $+$ $-$ \(q+\beta q^{3}+(-3+\beta )q^{5}-q^{7}-q^{9}+3\beta q^{11}+\cdots\)
5824.2.a.bl $2$ $46.505$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-6\) \(2\) $+$ $-$ $-$ \(q+\beta q^{3}+(-3-\beta )q^{5}+q^{7}-q^{9}+3\beta q^{11}+\cdots\)
5824.2.a.bm $2$ $46.505$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ \(q+\beta q^{3}+(1+\beta )q^{5}-q^{7}+3q^{9}+(-4+\cdots)q^{11}+\cdots\)
5824.2.a.bn $2$ $46.505$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ \(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+3q^{9}+(4+\cdots)q^{11}+\cdots\)
5824.2.a.bo $2$ $46.505$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(1\) \(2\) $-$ $-$ $+$ \(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
5824.2.a.bp $2$ $46.505$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $+$ $-$ \(q+(1+\beta )q^{3}-\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
5824.2.a.bq $2$ $46.505$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ \(q+(1+\beta )q^{3}+\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
5824.2.a.br $2$ $46.505$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(2\) \(2\) $+$ $-$ $+$ \(q+(2+\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+4\beta )q^{9}+\cdots\)
5824.2.a.bs $3$ $46.505$ 3.3.316.1 None \(0\) \(-2\) \(-2\) \(3\) $-$ $-$ $+$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+\cdots\)
5824.2.a.bt $3$ $46.505$ 3.3.564.1 None \(0\) \(-2\) \(-1\) \(-3\) $-$ $+$ $+$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
5824.2.a.bu $3$ $46.505$ 3.3.148.1 None \(0\) \(0\) \(-1\) \(-3\) $+$ $+$ $-$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
5824.2.a.bv $3$ $46.505$ 3.3.148.1 None \(0\) \(0\) \(-1\) \(3\) $+$ $-$ $-$ \(q-\beta _{2}q^{3}-\beta _{1}q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots\)
5824.2.a.bw $3$ $46.505$ 3.3.148.1 None \(0\) \(0\) \(5\) \(-3\) $+$ $+$ $+$ \(q-\beta _{2}q^{3}+(2-\beta _{1})q^{5}-q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.bx $3$ $46.505$ 3.3.148.1 None \(0\) \(0\) \(5\) \(3\) $+$ $-$ $+$ \(q+\beta _{2}q^{3}+(2-\beta _{1})q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.by $3$ $46.505$ 3.3.316.1 None \(0\) \(2\) \(-2\) \(-3\) $+$ $+$ $+$ \(q+(1-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+\cdots\)
5824.2.a.bz $3$ $46.505$ 3.3.564.1 None \(0\) \(2\) \(-1\) \(3\) $-$ $-$ $+$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
5824.2.a.ca $4$ $46.505$ 4.4.11348.1 None \(0\) \(-2\) \(1\) \(4\) $-$ $-$ $+$ \(q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.cb $4$ $46.505$ 4.4.64268.1 None \(0\) \(-1\) \(-2\) \(-4\) $+$ $+$ $-$ \(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.cc $4$ $46.505$ 4.4.183064.1 None \(0\) \(-1\) \(0\) \(4\) $+$ $-$ $+$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
5824.2.a.cd $4$ $46.505$ 4.4.33844.1 None \(0\) \(-1\) \(1\) \(4\) $-$ $-$ $-$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
5824.2.a.ce $4$ $46.505$ 4.4.64268.1 None \(0\) \(1\) \(-2\) \(4\) $-$ $-$ $-$ \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.cf $4$ $46.505$ 4.4.183064.1 None \(0\) \(1\) \(0\) \(-4\) $-$ $+$ $+$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
5824.2.a.cg $4$ $46.505$ 4.4.33844.1 None \(0\) \(1\) \(1\) \(-4\) $-$ $+$ $-$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
5824.2.a.ch $4$ $46.505$ 4.4.11348.1 None \(0\) \(2\) \(1\) \(-4\) $-$ $+$ $+$ \(q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.ci $5$ $46.505$ 5.5.1025428.1 None \(0\) \(-5\) \(3\) \(-5\) $-$ $+$ $-$ \(q+(-1-\beta _{1})q^{3}+(1-\beta _{4})q^{5}-q^{7}+\cdots\)
5824.2.a.cj $5$ $46.505$ 5.5.6329476.1 None \(0\) \(0\) \(-3\) \(-5\) $+$ $+$ $+$ \(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.ck $5$ $46.505$ 5.5.6329476.1 None \(0\) \(0\) \(-3\) \(5\) $+$ $-$ $+$ \(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5824.2.a.cl $5$ $46.505$ 5.5.1025428.1 None \(0\) \(5\) \(3\) \(5\) $-$ $-$ $-$ \(q+(1+\beta _{1})q^{3}+(1-\beta _{4})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
5824.2.a.cm $6$ $46.505$ 6.6.153499364.1 None \(0\) \(-4\) \(-3\) \(6\) $+$ $-$ $-$ \(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
5824.2.a.cn $6$ $46.505$ 6.6.153499364.1 None \(0\) \(4\) \(-3\) \(-6\) $+$ $+$ $-$ \(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5824))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5824)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2912))\)\(^{\oplus 2}\)