Properties

Label 196.4.a
Level $196$
Weight $4$
Character orbit 196.a
Rep. character $\chi_{196}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $7$
Sturm bound $112$
Trace bound $5$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 196.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(112\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(196))\).

Total New Old
Modular forms 96 10 86
Cusp forms 72 10 62
Eisenstein series 24 0 24

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.
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(6\)
Minus space\(-\)\(4\)

Trace form

\( 10q + 6q^{3} + 2q^{5} + 30q^{9} + O(q^{10}) \) \( 10q + 6q^{3} + 2q^{5} + 30q^{9} + 48q^{11} + 94q^{13} - 40q^{15} + 88q^{17} - 94q^{19} - 248q^{23} + 454q^{25} + 612q^{27} - 88q^{29} - 140q^{31} - 352q^{33} + 260q^{37} + 640q^{39} + 240q^{41} + 240q^{43} + 650q^{45} + 204q^{47} - 416q^{51} - 888q^{53} - 248q^{55} - 612q^{57} - 814q^{59} + 466q^{61} + 764q^{65} - 784q^{67} - 1504q^{69} + 1120q^{71} + 708q^{73} - 254q^{75} - 120q^{79} - 758q^{81} - 1046q^{83} + 160q^{85} - 1604q^{87} + 1788q^{89} + 1148q^{93} - 1016q^{95} - 1800q^{97} - 1816q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(196))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
196.4.a.a \(1\) \(11.564\) \(\Q\) None \(0\) \(-4\) \(-20\) \(0\) \(-\) \(-\) \(q-4q^{3}-20q^{5}-11q^{9}+44q^{11}+\cdots\)
196.4.a.b \(1\) \(11.564\) \(\Q\) None \(0\) \(-4\) \(-6\) \(0\) \(-\) \(-\) \(q-4q^{3}-6q^{5}-11q^{9}-12q^{11}+82q^{13}+\cdots\)
196.4.a.c \(1\) \(11.564\) \(\Q\) None \(0\) \(4\) \(20\) \(0\) \(-\) \(-\) \(q+4q^{3}+20q^{5}-11q^{9}+44q^{11}+\cdots\)
196.4.a.d \(1\) \(11.564\) \(\Q\) None \(0\) \(10\) \(8\) \(0\) \(-\) \(-\) \(q+10q^{3}+8q^{5}+73q^{9}-40q^{11}+\cdots\)
196.4.a.e \(2\) \(11.564\) \(\Q(\sqrt{37}) \) None \(0\) \(0\) \(-14\) \(0\) \(-\) \(+\) \(q-\beta q^{3}+(-7+2\beta )q^{5}+10q^{9}+(2^{4}+\cdots)q^{11}+\cdots\)
196.4.a.f \(2\) \(11.564\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta q^{3}-2\beta q^{5}-5^{2}q^{9}-26q^{11}+\cdots\)
196.4.a.g \(2\) \(11.564\) \(\Q(\sqrt{37}) \) None \(0\) \(0\) \(14\) \(0\) \(-\) \(-\) \(q-\beta q^{3}+(7+2\beta )q^{5}+10q^{9}+(2^{4}-7\beta )q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(196))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(196)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)