Properties

Label 28.4.a
Level $28$
Weight $4$
Character orbit 28.a
Rep. character $\chi_{28}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $16$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 28.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(28))\).

Total New Old
Modular forms 15 2 13
Cusp forms 9 2 7
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

\( 2 q - 6 q^{3} - 2 q^{5} + 62 q^{9} + O(q^{10}) \) \( 2 q - 6 q^{3} - 2 q^{5} + 62 q^{9} - 52 q^{11} - 94 q^{13} + 104 q^{15} - 88 q^{17} + 94 q^{19} + 98 q^{21} + 152 q^{23} - 150 q^{25} - 612 q^{27} + 184 q^{29} + 140 q^{31} + 352 q^{33} + 98 q^{35} + 136 q^{37} - 208 q^{39} - 240 q^{41} + 244 q^{43} - 650 q^{45} - 204 q^{47} + 98 q^{49} + 460 q^{51} + 108 q^{53} + 248 q^{55} + 12 q^{57} + 814 q^{59} - 466 q^{61} - 588 q^{63} - 396 q^{65} - 336 q^{67} + 1504 q^{69} - 1288 q^{71} - 708 q^{73} + 254 q^{75} + 196 q^{77} - 1144 q^{79} + 2318 q^{81} + 1046 q^{83} + 284 q^{85} + 1604 q^{87} - 1788 q^{89} - 490 q^{91} - 2968 q^{93} + 200 q^{95} + 1800 q^{97} - 2788 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(28))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
28.4.a.a $1$ $1.652$ \(\Q\) None \(0\) \(-10\) \(-8\) \(-7\) $-$ $+$ \(q-10q^{3}-8q^{5}-7q^{7}+73q^{9}-40q^{11}+\cdots\)
28.4.a.b $1$ $1.652$ \(\Q\) None \(0\) \(4\) \(6\) \(7\) $-$ $-$ \(q+4q^{3}+6q^{5}+7q^{7}-11q^{9}-12q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(28))\) into lower level spaces

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