Properties

Label 28.6.a
Level $28$
Weight $6$
Character orbit 28.a
Rep. character $\chi_{28}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 28.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(28))\).

Total New Old
Modular forms 23 2 21
Cusp forms 17 2 15
Eisenstein series 6 0 6

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

\(2\)\(7\)FrickeDim.
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(1\)

Trace form

\( 2 q + 24 q^{3} - 80 q^{5} + 194 q^{9} + O(q^{10}) \) \( 2 q + 24 q^{3} - 80 q^{5} + 194 q^{9} - 712 q^{11} + 1256 q^{13} + 608 q^{15} - 964 q^{17} - 2792 q^{19} - 1372 q^{21} + 3440 q^{23} + 3222 q^{25} + 5904 q^{27} - 7628 q^{29} - 1456 q^{31} + 1648 q^{33} - 5488 q^{35} - 22268 q^{37} + 16640 q^{39} + 25356 q^{41} - 10088 q^{43} + 29872 q^{45} - 24624 q^{47} + 4802 q^{49} - 60176 q^{51} + 14124 q^{53} + 69248 q^{55} - 69960 q^{57} + 35944 q^{59} + 6560 q^{61} - 32928 q^{63} - 43968 q^{65} + 51240 q^{67} + 86752 q^{69} + 25088 q^{71} - 32364 q^{73} - 86776 q^{75} - 35672 q^{77} + 17648 q^{79} + 79370 q^{81} + 63704 q^{83} - 155872 q^{85} - 75856 q^{87} - 25404 q^{89} - 5488 q^{91} + 136976 q^{93} - 34144 q^{95} + 124284 q^{97} + 175544 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(28))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
28.6.a.a $1$ $4.491$ \(\Q\) None \(0\) \(-2\) \(-96\) \(49\) $-$ $-$ \(q-2q^{3}-96q^{5}+7^{2}q^{7}-239q^{9}+\cdots\)
28.6.a.b $1$ $4.491$ \(\Q\) None \(0\) \(26\) \(16\) \(-49\) $-$ $+$ \(q+26q^{3}+2^{4}q^{5}-7^{2}q^{7}+433q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(28))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(28)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)