Properties

Label 28.10.a
Level $28$
Weight $10$
Character orbit 28.a
Rep. character $\chi_{28}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 28.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(28))\).

Total New Old
Modular forms 39 4 35
Cusp forms 33 4 29
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
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(2\)

Trace form

\( 4 q - 294 q^{3} + 3150 q^{5} + 7712 q^{9} + O(q^{10}) \) \( 4 q - 294 q^{3} + 3150 q^{5} + 7712 q^{9} + 11796 q^{11} - 62006 q^{13} - 135592 q^{15} - 78540 q^{17} + 566174 q^{19} - 369754 q^{21} - 241224 q^{23} + 5716992 q^{25} - 5935860 q^{27} - 4650852 q^{29} - 3677156 q^{31} + 13692784 q^{33} + 100842 q^{35} - 20278756 q^{37} + 35792768 q^{39} - 22213044 q^{41} - 23098756 q^{43} + 50202502 q^{45} + 34123908 q^{47} + 23059204 q^{49} - 163474196 q^{51} - 51210552 q^{53} + 30454648 q^{55} - 4482636 q^{57} + 254130030 q^{59} - 49895426 q^{61} + 88135908 q^{63} - 281225148 q^{65} + 9282168 q^{67} + 388112368 q^{69} - 232237320 q^{71} - 12708528 q^{73} - 87156706 q^{75} - 271264980 q^{77} - 381768008 q^{79} + 590930888 q^{81} + 676068582 q^{83} - 337114532 q^{85} - 250815628 q^{87} - 925489656 q^{89} - 738398738 q^{91} + 1218203672 q^{93} + 1975826616 q^{95} + 2994959604 q^{97} - 2672796508 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(28))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
28.10.a.a 28.a 1.a $2$ $14.421$ \(\Q(\sqrt{4561}) \) None \(0\) \(-224\) \(1596\) \(4802\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-112-\beta )q^{3}+(798+9\beta )q^{5}+7^{4}q^{7}+\cdots\)
28.10.a.b 28.a 1.a $2$ $14.421$ \(\Q(\sqrt{11209}) \) None \(0\) \(-70\) \(1554\) \(-4802\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-35-\beta )q^{3}+(777-19\beta )q^{5}-7^{4}q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(28))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(28)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)