Properties

Label 280.6.a
Level $280$
Weight $6$
Character orbit 280.a
Rep. character $\chi_{280}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $10$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(280))\).

Total New Old
Modular forms 248 30 218
Cusp forms 232 30 202
Eisenstein series 16 0 16

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

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(14\)
Minus space\(-\)\(16\)

Trace form

\( 30q + 44q^{3} + 2298q^{9} + O(q^{10}) \) \( 30q + 44q^{3} + 2298q^{9} - 916q^{11} - 3012q^{17} - 1788q^{19} - 2152q^{23} + 18750q^{25} + 176q^{27} + 3888q^{31} + 22776q^{33} + 7350q^{35} - 5476q^{37} + 10020q^{39} - 17164q^{41} + 24008q^{43} + 20144q^{47} + 72030q^{49} - 76388q^{51} - 7540q^{53} + 27800q^{55} + 7128q^{57} - 105956q^{59} - 16784q^{61} - 33800q^{65} + 68256q^{67} + 78104q^{69} - 43896q^{71} + 278108q^{73} + 27500q^{75} - 47432q^{77} - 238228q^{79} + 164398q^{81} - 179492q^{83} - 28900q^{85} + 8496q^{87} + 685268q^{89} + 54488q^{91} + 185240q^{93} + 37900q^{95} - 423524q^{97} - 225464q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(280))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
280.6.a.a \(1\) \(44.907\) \(\Q\) None \(0\) \(-12\) \(25\) \(-49\) \(+\) \(-\) \(+\) \(q-12q^{3}+5^{2}q^{5}-7^{2}q^{7}-99q^{9}+\cdots\)
280.6.a.b \(1\) \(44.907\) \(\Q\) None \(0\) \(4\) \(25\) \(-49\) \(-\) \(-\) \(+\) \(q+4q^{3}+5^{2}q^{5}-7^{2}q^{7}-227q^{9}+\cdots\)
280.6.a.c \(2\) \(44.907\) \(\Q(\sqrt{109}) \) None \(0\) \(2\) \(50\) \(-98\) \(-\) \(-\) \(+\) \(q+(1+\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(194+\cdots)q^{9}+\cdots\)
280.6.a.d \(2\) \(44.907\) \(\Q(\sqrt{37}) \) None \(0\) \(26\) \(50\) \(-98\) \(+\) \(-\) \(+\) \(q+(13-\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(74+\cdots)q^{9}+\cdots\)
280.6.a.e \(3\) \(44.907\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(6\) \(-75\) \(147\) \(-\) \(+\) \(-\) \(q+(2-\beta _{1})q^{3}-5^{2}q^{5}+7^{2}q^{7}+(70+\cdots)q^{9}+\cdots\)
280.6.a.f \(3\) \(44.907\) 3.3.996509.1 None \(0\) \(14\) \(-75\) \(147\) \(+\) \(+\) \(-\) \(q+(5+\beta _{2})q^{3}-5^{2}q^{5}+7^{2}q^{7}+(4+3\beta _{1}+\cdots)q^{9}+\cdots\)
280.6.a.g \(4\) \(44.907\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-13\) \(100\) \(196\) \(+\) \(-\) \(-\) \(q+(-3-\beta _{1})q^{3}+5^{2}q^{5}+7^{2}q^{7}+(-7^{2}+\cdots)q^{9}+\cdots\)
280.6.a.h \(4\) \(44.907\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(5\) \(-100\) \(-196\) \(+\) \(+\) \(+\) \(q+(1+\beta _{1})q^{3}-5^{2}q^{5}-7^{2}q^{7}+(142+\cdots)q^{9}+\cdots\)
280.6.a.i \(5\) \(44.907\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-3\) \(-125\) \(-245\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}-5^{2}q^{5}-7^{2}q^{7}+(74+\cdots)q^{9}+\cdots\)
280.6.a.j \(5\) \(44.907\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(15\) \(125\) \(245\) \(-\) \(-\) \(-\) \(q+(3-\beta _{1})q^{3}+5^{2}q^{5}+7^{2}q^{7}+(226+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(280))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(280)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)