Properties

Label 6724.2.a
Level $6724$
Weight $2$
Character orbit 6724.a
Rep. character $\chi_{6724}(1,\cdot)$
Character field $\Q$
Dimension $136$
Newform subspaces $13$
Sturm bound $1722$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 6724 = 2^{2} \cdot 41^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6724.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(1722\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6724))\).

Total New Old
Modular forms 924 136 788
Cusp forms 799 136 663
Eisenstein series 125 0 125

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

\(2\)\(41\)FrickeDim.
\(-\)\(+\)\(-\)\(73\)
\(-\)\(-\)\(+\)\(63\)
Plus space\(+\)\(63\)
Minus space\(-\)\(73\)

Trace form

\( 136q - 2q^{3} - 4q^{5} + 128q^{9} + O(q^{10}) \) \( 136q - 2q^{3} - 4q^{5} + 128q^{9} - 4q^{11} + 10q^{15} + 4q^{17} - 6q^{19} + 12q^{23} + 128q^{25} + 10q^{27} + 4q^{29} + 10q^{31} + 22q^{33} + 26q^{35} - 14q^{37} + 24q^{39} - 2q^{43} - 12q^{45} + 6q^{47} + 124q^{49} + 6q^{51} + 16q^{53} + 2q^{55} - 12q^{57} - 12q^{59} - 22q^{61} + 10q^{63} - 4q^{65} - 28q^{67} + 28q^{69} + 2q^{71} - 6q^{73} - 30q^{75} - 16q^{77} + 18q^{79} + 112q^{81} + 8q^{83} - 32q^{85} - 42q^{87} - 4q^{89} - 40q^{91} + 28q^{93} - 14q^{95} - 16q^{97} - 58q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6724))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 41
6724.2.a.a \(3\) \(53.691\) 3.3.785.1 None \(0\) \(-2\) \(-2\) \(7\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1})q^{5}+(2+\cdots)q^{7}+\cdots\)
6724.2.a.b \(3\) \(53.691\) 3.3.785.1 None \(0\) \(2\) \(-2\) \(-7\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{1})q^{5}+(-2+\cdots)q^{7}+\cdots\)
6724.2.a.c \(4\) \(53.691\) 4.4.25808.1 None \(0\) \(-2\) \(4\) \(0\) \(-\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{3}+(2-\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
6724.2.a.d \(4\) \(53.691\) 4.4.25088.1 None \(0\) \(0\) \(4\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots\)
6724.2.a.e \(6\) \(53.691\) 6.6.40716288.1 None \(0\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
6724.2.a.f \(8\) \(53.691\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{2}+\beta _{5}+\beta _{6}+\beta _{7})q^{7}+\cdots\)
6724.2.a.g \(8\) \(53.691\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(3\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}-\beta _{6}q^{5}+(-\beta _{2}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
6724.2.a.h \(12\) \(53.691\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(-\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{4}+\beta _{10})q^{7}+(1+\cdots)q^{9}+\cdots\)
6724.2.a.i \(12\) \(53.691\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(1\) \(-2\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{4}-\beta _{10})q^{7}+\cdots\)
6724.2.a.j \(16\) \(53.691\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(\beta _{1}-\beta _{11})q^{7}+(2+\cdots)q^{9}+\cdots\)
6724.2.a.k \(18\) \(53.691\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-5\) \(2\) \(-7\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(1+\beta _{4}+\beta _{7}+\beta _{12}-\beta _{17})q^{5}+\cdots\)
6724.2.a.l \(18\) \(53.691\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(5\) \(2\) \(7\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{4}+\beta _{7}+\beta _{12}-\beta _{17})q^{5}+\cdots\)
6724.2.a.m \(24\) \(53.691\) None \(0\) \(0\) \(-16\) \(0\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6724))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6724)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1681))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3362))\)\(^{\oplus 2}\)