↑

Properties

Label 334.2.a
Level $334$
Weight $2$
Character orbit 334.a
Rep. character $\chi_{334}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $6$
Sturm bound $84$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 334 = 2 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 334.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(84\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(334))\).

Total New Old
Modular forms 44 13 31
Cusp forms 41 13 28
Eisenstein series 3 0 3

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

\(2\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(9\)

Trace form

\( 13q - q^{2} - 4q^{3} + 13q^{4} - 4q^{5} - 8q^{7} - q^{8} + 13q^{9} + O(q^{10}) \) \( 13q - q^{2} - 4q^{3} + 13q^{4} - 4q^{5} - 8q^{7} - q^{8} + 13q^{9} - 4q^{10} + 4q^{11} - 4q^{12} + 4q^{14} + 4q^{15} + 13q^{16} + 10q^{17} - 5q^{18} - 4q^{19} - 4q^{20} + 16q^{21} - 8q^{22} + 4q^{23} - q^{25} + 4q^{26} - 4q^{27} - 8q^{28} - 2q^{29} - 4q^{30} - 12q^{31} - q^{32} + 8q^{33} - 6q^{34} + 32q^{35} + 13q^{36} - 12q^{37} - 4q^{38} + 4q^{39} - 4q^{40} + 26q^{41} + 4q^{42} - 6q^{43} + 4q^{44} - 4q^{45} + 8q^{46} - 8q^{47} - 4q^{48} - 15q^{49} + q^{50} - 4q^{51} + 12q^{53} - 12q^{54} - 12q^{55} + 4q^{56} - 4q^{57} - 30q^{58} + 18q^{59} + 4q^{60} - 10q^{61} + 8q^{62} - 40q^{63} + 13q^{64} - 28q^{65} - 16q^{66} - 14q^{67} + 10q^{68} - 16q^{69} - 8q^{70} - 4q^{71} - 5q^{72} - 38q^{73} - 8q^{74} - 44q^{75} - 4q^{76} + 24q^{77} - 4q^{78} - 4q^{80} - 19q^{81} - 14q^{82} + 10q^{83} + 16q^{84} + 8q^{85} - 10q^{86} + 28q^{87} - 8q^{88} + 22q^{89} - 16q^{91} + 4q^{92} - 40q^{93} + 20q^{94} + 32q^{95} - 10q^{97} - 25q^{98} + 28q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(334))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 167
334.2.a.a \(1\) \(2.667\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
334.2.a.b \(2\) \(2.667\) \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
334.2.a.c \(2\) \(2.667\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-6\) \(+\) \(-\) \(q-q^{2}+2\beta q^{3}+q^{4}+(1-\beta )q^{5}-2\beta q^{6}+\cdots\)
334.2.a.d \(2\) \(2.667\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-4\) \(-6\) \(-\) \(-\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
334.2.a.e \(3\) \(2.667\) 3.3.469.1 None \(-3\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
334.2.a.f \(3\) \(2.667\) 3.3.733.1 None \(3\) \(1\) \(-3\) \(3\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(334))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(334)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 2}\)