Properties

Label 338.2.b
Level $338$
Weight $2$
Character orbit 338.b
Rep. character $\chi_{338}(337,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $91$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 338.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(91\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(338, [\chi])\).

Total New Old
Modular forms 60 12 48
Cusp forms 32 12 20
Eisenstein series 28 0 28

Trace form

\( 12q + 2q^{3} - 12q^{4} + 18q^{9} + O(q^{10}) \) \( 12q + 2q^{3} - 12q^{4} + 18q^{9} - 6q^{10} - 2q^{12} + 4q^{14} + 12q^{16} - 4q^{17} - 2q^{22} + 16q^{23} - 2q^{25} - 16q^{27} - 6q^{29} + 12q^{30} - 28q^{35} - 18q^{36} - 10q^{38} + 6q^{40} - 12q^{42} + 6q^{43} + 2q^{48} + 20q^{51} + 6q^{53} - 8q^{55} - 4q^{56} + 6q^{61} + 8q^{62} - 12q^{64} - 8q^{66} + 4q^{68} + 4q^{69} - 2q^{74} + 14q^{75} + 20q^{77} - 36q^{79} - 12q^{81} + 4q^{82} - 20q^{87} + 2q^{88} + 26q^{90} - 16q^{92} + 60q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(338, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
338.2.b.a \(2\) \(2.699\) \(\Q(\sqrt{-1}) \) None \(0\) \(-6\) \(0\) \(0\) \(q+iq^{2}-3q^{3}-q^{4}-iq^{5}-3iq^{6}+\cdots\)
338.2.b.b \(2\) \(2.699\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{5}-4iq^{7}-iq^{8}+\cdots\)
338.2.b.c \(2\) \(2.699\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+3iq^{5}+iq^{6}+\cdots\)
338.2.b.d \(6\) \(2.699\) 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{4})q^{3}-q^{4}-2\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(338, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)