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Properties

Label 740.2.be
Level $740$
Weight $2$
Character orbit 740.be
Rep. character $\chi_{740}(51,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
Newform subspaces $1$
Sturm bound $228$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 740.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 148 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(228\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(740, [\chi])\).

Total New Old
Modular forms 472 304 168
Cusp forms 440 304 136
Eisenstein series 32 0 32

Trace form

\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(740, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
740.2.be.a 740.be 148.l $304$ $5.909$ None 740.2.be.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(740, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(740, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 2}\)