Properties

Label 429.2.a
Level $429$
Weight $2$
Character orbit 429.a
Rep. character $\chi_{429}(1,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $8$
Sturm bound $112$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(429))\).

Total New Old
Modular forms 60 19 41
Cusp forms 53 19 34
Eisenstein series 7 0 7

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

\(3\)\(11\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(13\)

Trace form

\( 19q - 3q^{2} - q^{3} + 21q^{4} - 6q^{5} + 5q^{6} - 8q^{7} + 9q^{8} + 19q^{9} + O(q^{10}) \) \( 19q - 3q^{2} - q^{3} + 21q^{4} - 6q^{5} + 5q^{6} - 8q^{7} + 9q^{8} + 19q^{9} + 14q^{10} - q^{11} - 7q^{12} - q^{13} + 2q^{15} + 13q^{16} - 10q^{17} - 3q^{18} + 4q^{19} - 18q^{20} - 8q^{21} - 3q^{22} - 8q^{23} + 9q^{24} - 3q^{25} - 3q^{26} - q^{27} + 2q^{29} + 14q^{30} + 24q^{31} - 15q^{32} + 3q^{33} + 18q^{34} + 56q^{35} + 21q^{36} - 14q^{37} + 12q^{38} - q^{39} + 14q^{40} - 2q^{41} - 16q^{42} + 4q^{43} - 7q^{44} - 6q^{45} - 40q^{46} + 24q^{47} + q^{48} - 5q^{49} - 37q^{50} - 2q^{51} - 7q^{52} - 14q^{53} + 5q^{54} - 6q^{55} - 16q^{56} - 20q^{57} + 14q^{58} + 20q^{59} - 18q^{60} - 22q^{61} + 16q^{62} - 8q^{63} - 3q^{64} + 2q^{65} - 3q^{66} + 28q^{67} - 14q^{68} + 24q^{69} - 40q^{70} + 16q^{71} + 9q^{72} - 26q^{73} - 42q^{74} - 15q^{75} + 20q^{76} + q^{78} + 8q^{79} - 74q^{80} + 19q^{81} - 22q^{82} + 28q^{83} - 24q^{84} - 20q^{85} + 12q^{86} - 14q^{87} - 15q^{88} - 50q^{89} + 14q^{90} + 8q^{91} - 40q^{92} - 8q^{93} - 48q^{94} + 48q^{95} + 33q^{96} - 18q^{97} - 27q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(429))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11 13
429.2.a.a \(1\) \(3.426\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
429.2.a.b \(1\) \(3.426\) \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots\)
429.2.a.c \(2\) \(3.426\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-4\) \(-4\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
429.2.a.d \(2\) \(3.426\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-4\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
429.2.a.e \(3\) \(3.426\) 3.3.564.1 None \(-1\) \(-3\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
429.2.a.f \(3\) \(3.426\) 3.3.148.1 None \(1\) \(3\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
429.2.a.g \(3\) \(3.426\) 3.3.148.1 None \(3\) \(3\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
429.2.a.h \(4\) \(3.426\) 4.4.8468.1 None \(-2\) \(-4\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(429))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(429)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 2}\)