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 about

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

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

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

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