Properties

Label 1470.2.b
Level $1470$
Weight $2$
Character orbit 1470.b
Rep. character $\chi_{1470}(881,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $4$
Sturm bound $672$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(672\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

Total New Old
Modular forms 368 56 312
Cusp forms 304 56 248
Eisenstein series 64 0 64

Trace form

\( 56q - 56q^{4} + 4q^{9} + O(q^{10}) \) \( 56q - 56q^{4} + 4q^{9} + 8q^{15} + 56q^{16} + 16q^{18} + 56q^{25} + 4q^{30} - 4q^{36} + 32q^{37} + 24q^{39} + 32q^{43} - 40q^{46} + 40q^{51} - 8q^{57} - 8q^{60} - 56q^{64} + 48q^{67} - 16q^{72} - 80q^{79} - 4q^{81} - 48q^{85} - 72q^{93} + 80q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1470.2.b.a \(12\) \(11.738\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(12\) \(0\) \(q+\beta _{4}q^{2}-\beta _{1}q^{3}-q^{4}+q^{5}-\beta _{9}q^{6}+\cdots\)
1470.2.b.b \(12\) \(11.738\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(4\) \(-12\) \(0\) \(q+\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}-q^{5}+\beta _{9}q^{6}+\cdots\)
1470.2.b.c \(16\) \(11.738\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-8\) \(-16\) \(0\) \(q-\beta _{9}q^{2}-\beta _{11}q^{3}-q^{4}-q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots\)
1470.2.b.d \(16\) \(11.738\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(8\) \(16\) \(0\) \(q-\beta _{9}q^{2}+\beta _{11}q^{3}-q^{4}+q^{5}+(\beta _{5}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)