Properties

Label 322.2.c
Level $322$
Weight $2$
Character orbit 322.c
Rep. character $\chi_{322}(321,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $96$
Trace bound $23$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(322, [\chi])\).

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

Trace form

\( 16q + 16q^{4} - 8q^{9} + O(q^{10}) \) \( 16q + 16q^{4} - 8q^{9} + 16q^{16} - 24q^{18} + 8q^{23} + 8q^{25} - 24q^{29} + 8q^{35} - 8q^{36} + 16q^{39} + 16q^{49} - 24q^{50} - 8q^{58} + 16q^{64} + 8q^{70} + 16q^{71} - 24q^{72} - 16q^{77} + 8q^{81} - 104q^{85} + 8q^{92} - 104q^{93} - 64q^{95} + 16q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(322, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
322.2.c.a \(4\) \(2.571\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots\)
322.2.c.b \(4\) \(2.571\) \(\Q(\sqrt{-2}, \sqrt{-7})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
322.2.c.c \(4\) \(2.571\) 4.0.2312.1 None \(4\) \(0\) \(-8\) \(-2\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}-2q^{5}-\beta _{2}q^{6}+\cdots\)
322.2.c.d \(4\) \(2.571\) 4.0.2312.1 None \(4\) \(0\) \(8\) \(2\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}+2q^{5}-\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(322, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(322, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)