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Properties

Label 333.3.bb
Level $333$
Weight $3$
Character orbit 333.bb
Rep. character $\chi_{333}(82,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $120$
Newform subspaces $4$
Sturm bound $114$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 333 = 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 333.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(114\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(333, [\chi])\).

Total New Old
Modular forms 320 128 192
Cusp forms 288 120 168
Eisenstein series 32 8 24

Trace form

\( 120 q + 8 q^{2} - 24 q^{4} + 2 q^{5} - 2 q^{7} + 48 q^{8} + O(q^{10}) \) \( 120 q + 8 q^{2} - 24 q^{4} + 2 q^{5} - 2 q^{7} + 48 q^{8} + 4 q^{10} - 28 q^{13} - 52 q^{14} + 164 q^{16} - 24 q^{17} + 76 q^{19} + 26 q^{20} + 4 q^{22} - 36 q^{23} + 120 q^{25} + 112 q^{26} - 54 q^{28} + 20 q^{29} + 72 q^{31} - 152 q^{32} + 206 q^{35} + 254 q^{37} - 104 q^{38} - 138 q^{40} + 108 q^{41} - 120 q^{43} + 124 q^{44} + 238 q^{46} - 416 q^{47} - 380 q^{49} + 60 q^{50} - 228 q^{52} + 36 q^{53} + 64 q^{55} - 250 q^{56} + 114 q^{58} + 220 q^{59} + 282 q^{61} + 120 q^{62} - 48 q^{65} - 336 q^{67} + 444 q^{68} - 130 q^{70} - 22 q^{71} - 96 q^{74} + 228 q^{76} - 720 q^{77} - 204 q^{79} + 700 q^{80} - 532 q^{82} - 86 q^{83} - 178 q^{86} - 188 q^{88} - 192 q^{89} + 404 q^{91} + 202 q^{92} - 132 q^{94} - 708 q^{95} - 124 q^{97} - 1424 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(333, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
333.3.bb.a 333.bb 37.g $24$ $9.074$ None 37.3.g.a \(0\) \(0\) \(18\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
333.3.bb.b 333.bb 37.g $24$ $9.074$ None 111.3.l.b \(4\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
333.3.bb.c 333.bb 37.g $24$ $9.074$ None 111.3.l.a \(4\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
333.3.bb.d 333.bb 37.g $48$ $9.074$ None 333.3.bb.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{3}^{\mathrm{old}}(333, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(333, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)