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Properties

Label 212.2.b
Level $212$
Weight $2$
Character orbit 212.b
Rep. character $\chi_{212}(105,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $54$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 212 = 2^{2} \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 212.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 53 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(54\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(212, [\chi])\).

Total New Old
Modular forms 30 4 26
Cusp forms 24 4 20
Eisenstein series 6 0 6

Trace form

\( 4 q + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 4 q^{15} + 12 q^{17} - 20 q^{25} + 8 q^{29} + 8 q^{37} + 12 q^{43} - 24 q^{47} - 12 q^{49} - 8 q^{53} - 20 q^{57} + 24 q^{59} + 8 q^{63} - 12 q^{69} + 8 q^{77} - 32 q^{81} - 8 q^{89} - 28 q^{91} + 36 q^{93} + 44 q^{95} + 32 q^{97} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(212, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
212.2.b.a 212.b 53.b $4$ $1.693$ 4.0.29952.1 None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(212, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(212, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 2}\)