Properties

Label 210.2.j
Level $210$
Weight $2$
Character orbit 210.j
Rep. character $\chi_{210}(113,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $2$
Sturm bound $96$
Trace bound $5$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).

Total New Old
Modular forms 112 24 88
Cusp forms 80 24 56
Eisenstein series 32 0 32

Trace form

\( 24q + 8q^{3} + O(q^{10}) \) \( 24q + 8q^{3} - 8q^{12} + 8q^{15} - 24q^{16} - 8q^{18} - 8q^{21} + 8q^{22} + 40q^{25} + 8q^{27} - 16q^{31} - 32q^{33} + 8q^{36} - 40q^{37} - 16q^{40} + 16q^{43} - 40q^{45} + 16q^{46} - 8q^{48} + 16q^{51} - 32q^{55} + 32q^{57} - 16q^{58} + 8q^{63} - 16q^{66} + 8q^{70} + 8q^{72} - 48q^{73} + 32q^{75} - 8q^{78} - 72q^{81} + 64q^{82} - 72q^{85} - 80q^{87} + 8q^{88} + 40q^{90} + 48q^{91} + 56q^{93} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
210.2.j.a \(12\) \(1.677\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(4\) \(-4\) \(0\) \(q+\beta _{2}q^{2}+\beta _{11}q^{3}-\beta _{7}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
210.2.j.b \(12\) \(1.677\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(4\) \(4\) \(0\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{7}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)