Properties

Label 714.2.f
Level $714$
Weight $2$
Character orbit 714.f
Rep. character $\chi_{714}(545,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $2$
Sturm bound $288$
Trace bound $17$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 714.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(714, [\chi])\).

Total New Old
Modular forms 152 40 112
Cusp forms 136 40 96
Eisenstein series 16 0 16

Trace form

\( 40 q - 40 q^{4} + 8 q^{7} + 8 q^{9} + O(q^{10}) \) \( 40 q - 40 q^{4} + 8 q^{7} + 8 q^{9} + 8 q^{15} + 40 q^{16} - 16 q^{18} + 4 q^{21} + 8 q^{22} + 32 q^{25} - 8 q^{28} - 8 q^{36} + 40 q^{37} + 48 q^{39} + 20 q^{42} + 40 q^{43} + 48 q^{46} + 16 q^{57} - 56 q^{58} - 8 q^{60} + 16 q^{63} - 40 q^{64} - 88 q^{67} - 48 q^{70} + 16 q^{72} - 40 q^{78} + 72 q^{81} - 4 q^{84} - 8 q^{88} - 40 q^{91} - 40 q^{93} - 72 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(714, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
714.2.f.a 714.f 21.c $20$ $5.701$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{9}q^{3}-q^{4}+\beta _{14}q^{5}+\beta _{6}q^{6}+\cdots\)
714.2.f.b 714.f 21.c $20$ $5.701$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}-q^{4}-\beta _{14}q^{5}+\beta _{10}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(714, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)