Properties

Label 2014.2.b
Level $2014$
Weight $2$
Character orbit 2014.b
Rep. character $\chi_{2014}(1483,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $4$
Sturm bound $540$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2014 = 2 \cdot 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2014.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 53 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(540\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2014, [\chi])\).

Total New Old
Modular forms 274 82 192
Cusp forms 266 82 184
Eisenstein series 8 0 8

Trace form

\( 82 q - 82 q^{4} - 4 q^{6} - 8 q^{7} - 94 q^{9} + O(q^{10}) \) \( 82 q - 82 q^{4} - 4 q^{6} - 8 q^{7} - 94 q^{9} - 12 q^{11} + 16 q^{13} - 8 q^{15} + 82 q^{16} - 16 q^{17} + 4 q^{24} - 94 q^{25} + 8 q^{28} + 8 q^{29} + 94 q^{36} + 48 q^{37} - 6 q^{38} - 28 q^{42} + 4 q^{43} + 12 q^{44} - 16 q^{46} + 20 q^{47} + 50 q^{49} - 16 q^{52} - 24 q^{53} + 4 q^{54} - 4 q^{57} - 32 q^{59} + 8 q^{60} - 16 q^{62} - 52 q^{63} - 82 q^{64} + 24 q^{66} + 16 q^{68} - 80 q^{69} + 8 q^{70} + 16 q^{77} + 80 q^{78} + 130 q^{81} + 16 q^{89} - 8 q^{90} - 104 q^{93} - 4 q^{96} - 32 q^{97} + 52 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2014, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2014.2.b.a 2014.b 53.b $2$ $16.082$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}-4q^{7}-iq^{8}+\cdots\)
2014.2.b.b 2014.b 53.b $6$ $16.082$ 6.0.62094400.1 None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{4}+\beta _{4}q^{5}+(1+\beta _{2})q^{7}+\cdots\)
2014.2.b.c 2014.b 53.b $30$ $16.082$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$
2014.2.b.d 2014.b 53.b $44$ $16.082$ None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1007, [\chi])\)\(^{\oplus 2}\)