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Properties

Label 276.3.f
Level $276$
Weight $3$
Character orbit 276.f
Rep. character $\chi_{276}(139,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 276.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(276, [\chi])\).

Total New Old
Modular forms 100 44 56
Cusp forms 92 44 48
Eisenstein series 8 0 8

Trace form

\( 44 q + 8 q^{5} - 12 q^{8} - 132 q^{9} + O(q^{10}) \) \( 44 q + 8 q^{5} - 12 q^{8} - 132 q^{9} - 28 q^{10} + 24 q^{12} - 8 q^{13} + 76 q^{14} + 8 q^{16} - 40 q^{17} + 4 q^{20} - 48 q^{21} - 44 q^{22} + 36 q^{24} + 324 q^{25} - 112 q^{26} - 168 q^{28} + 40 q^{29} + 72 q^{30} - 20 q^{32} + 48 q^{33} + 88 q^{37} - 4 q^{38} + 172 q^{40} - 200 q^{41} + 108 q^{42} + 176 q^{44} - 24 q^{45} - 436 q^{49} - 40 q^{50} - 152 q^{52} - 24 q^{53} - 236 q^{56} + 144 q^{57} + 192 q^{58} + 72 q^{60} - 168 q^{61} - 80 q^{62} - 120 q^{64} + 176 q^{65} - 192 q^{66} + 460 q^{68} - 408 q^{70} + 36 q^{72} + 184 q^{73} + 480 q^{74} - 164 q^{76} + 160 q^{77} - 24 q^{78} - 260 q^{80} + 396 q^{81} + 152 q^{82} - 216 q^{84} + 16 q^{85} - 36 q^{86} + 300 q^{88} - 520 q^{89} + 84 q^{90} + 144 q^{93} - 440 q^{94} - 180 q^{96} - 104 q^{97} - 320 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(276, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
276.3.f.a 276.f 4.b $4$ $7.520$ \(\Q(\sqrt{-3}, \sqrt{-23})\) None 276.3.f.a \(-4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+(-2+2\beta _{1}+\cdots)q^{4}+\cdots\)
276.3.f.b 276.f 4.b $40$ $7.520$ None 276.3.f.b \(4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(276, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(276, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)