Properties

Label 210.2.b
Level $210$
Weight $2$
Character orbit 210.b
Rep. character $\chi_{210}(41,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(17\)

Dimensions

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

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

Trace form

\( 8q - 8q^{4} + 12q^{7} + O(q^{10}) \) \( 8q - 8q^{4} + 12q^{7} - 4q^{15} + 8q^{16} - 16q^{18} - 16q^{21} + 8q^{25} - 12q^{28} - 4q^{30} + 24q^{37} - 24q^{39} - 4q^{42} + 32q^{43} + 32q^{46} - 32q^{51} + 24q^{57} + 8q^{58} + 4q^{60} + 20q^{63} - 8q^{64} - 96q^{67} - 12q^{70} + 16q^{72} - 16q^{78} + 8q^{81} + 16q^{84} + 24q^{85} - 32q^{91} + 40q^{93} + O(q^{100}) \)

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.b.a \(4\) \(1.677\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(4\) \(6\) \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+q^{5}+\cdots\)
210.2.b.b \(4\) \(1.677\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(-4\) \(6\) \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}-q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)