Properties

Label 728.2.a
Level 728
Weight 2
Character orbit a
Rep. character \(\chi_{728}(1,\cdot)\)
Character field \(\Q\)
Dimension 18
Newforms 9
Sturm bound 224
Trace bound 5

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Defining parameters

Level: \( N \) = \( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 728.a (trivial)
Character field: \(\Q\)
Newforms: \( 9 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(728))\).

Total New Old
Modular forms 120 18 102
Cusp forms 105 18 87
Eisenstein series 15 0 15

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.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(6\)
Minus space\(-\)\(12\)

Trace form

\(18q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 30q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 30q^{9} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 10q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 24q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut +\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 36q^{59} \) \(\mathstrut -\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 12q^{73} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 50q^{81} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 48q^{87} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut -\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(728))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 13
728.2.a.a \(1\) \(5.813\) \(\Q\) None \(0\) \(-2\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q-2q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
728.2.a.b \(1\) \(5.813\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
728.2.a.c \(1\) \(5.813\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{5}-q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
728.2.a.d \(1\) \(5.813\) \(\Q\) None \(0\) \(2\) \(3\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{3}+3q^{5}+q^{7}+q^{9}-q^{13}+6q^{15}+\cdots\)
728.2.a.e \(2\) \(5.813\) \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(q+(-2+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+\cdots\)
728.2.a.f \(2\) \(5.813\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q+(-1+\beta )q^{3}-\beta q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
728.2.a.g \(2\) \(5.813\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
728.2.a.h \(4\) \(5.813\) 4.4.183064.1 None \(0\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
728.2.a.i \(4\) \(5.813\) 4.4.64268.1 None \(0\) \(1\) \(2\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}-q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(728))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(728)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 2}\)