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Properties

Label 3234.2.e
Level $3234$
Weight $2$
Character orbit 3234.e
Rep. character $\chi_{3234}(2155,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $4$
Sturm bound $1344$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1344\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 704 80 624
Cusp forms 640 80 560
Eisenstein series 64 0 64

Trace form

\( 80 q - 80 q^{4} - 80 q^{9} + O(q^{10}) \) \( 80 q - 80 q^{4} - 80 q^{9} + 16 q^{11} - 8 q^{15} + 80 q^{16} - 12 q^{22} + 16 q^{23} - 56 q^{25} + 80 q^{36} - 24 q^{37} - 16 q^{44} + 8 q^{60} - 80 q^{64} - 64 q^{67} + 16 q^{71} + 80 q^{81} + 48 q^{86} + 12 q^{88} - 16 q^{92} - 48 q^{93} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3234.2.e.a 3234.e 77.b $16$ $25.824$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{12}q^{2}-\beta _{12}q^{3}-q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots\)
3234.2.e.b 3234.e 77.b $16$ $25.824$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{12}q^{2}-\beta _{12}q^{3}-q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots\)
3234.2.e.c 3234.e 77.b $24$ $25.824$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
3234.2.e.d 3234.e 77.b $24$ $25.824$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \)