Properties

Label 276.2.c
Level $276$
Weight $2$
Character orbit 276.c
Rep. character $\chi_{276}(47,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $2$
Sturm bound $96$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(276, [\chi])\).

Total New Old
Modular forms 52 44 8
Cusp forms 44 44 0
Eisenstein series 8 0 8

Trace form

\( 44 q - 3 q^{6} - 4 q^{9} + O(q^{10}) \) \( 44 q - 3 q^{6} - 4 q^{9} + 8 q^{10} + 7 q^{12} - 8 q^{13} + 8 q^{16} - q^{18} + 4 q^{22} - 8 q^{24} - 36 q^{25} + 12 q^{28} + 10 q^{30} - 16 q^{33} - 12 q^{34} - 33 q^{36} - 8 q^{37} - 8 q^{40} - 12 q^{42} - 5 q^{48} - 28 q^{49} - 38 q^{52} - 32 q^{54} + 24 q^{57} + 6 q^{58} + 36 q^{60} + 24 q^{61} + 6 q^{64} + 42 q^{66} + 12 q^{72} - 8 q^{73} + 52 q^{76} - 35 q^{78} + 20 q^{81} - 58 q^{82} + 38 q^{84} + 16 q^{85} - 60 q^{88} + 58 q^{90} + 24 q^{93} - 26 q^{94} - 27 q^{96} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(276, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
276.2.c.a 276.c 12.b $22$ $2.204$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
276.2.c.b 276.c 12.b $22$ $2.204$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$