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Properties

Label 294.3.o
Level $294$
Weight $3$
Character orbit 294.o
Rep. character $\chi_{294}(61,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $216$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 294.o (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(294, [\chi])\).

Total New Old
Modular forms 1392 216 1176
Cusp forms 1296 216 1080
Eisenstein series 96 0 96

Trace form

\( 216 q - 6 q^{3} + 36 q^{4} - 12 q^{5} + 10 q^{7} - 54 q^{9} + O(q^{10}) \) \( 216 q - 6 q^{3} + 36 q^{4} - 12 q^{5} + 10 q^{7} - 54 q^{9} + 24 q^{10} + 152 q^{11} + 12 q^{12} - 24 q^{14} + 60 q^{15} + 72 q^{16} - 148 q^{17} + 42 q^{19} - 56 q^{20} - 128 q^{22} - 16 q^{23} - 110 q^{25} + 128 q^{26} - 40 q^{28} + 80 q^{29} - 102 q^{31} + 36 q^{33} - 172 q^{35} + 216 q^{36} + 192 q^{37} + 536 q^{38} + 540 q^{39} + 176 q^{40} + 784 q^{41} + 312 q^{42} - 188 q^{43} + 248 q^{44} + 132 q^{45} + 48 q^{46} + 832 q^{47} - 110 q^{49} + 128 q^{50} - 312 q^{51} - 68 q^{52} - 528 q^{53} - 1120 q^{55} - 400 q^{56} + 180 q^{57} - 584 q^{58} - 816 q^{59} - 312 q^{60} - 838 q^{61} - 784 q^{62} - 240 q^{63} - 288 q^{64} - 140 q^{65} - 198 q^{67} - 96 q^{68} + 128 q^{70} - 184 q^{71} + 318 q^{73} - 528 q^{74} - 66 q^{75} - 540 q^{77} + 240 q^{78} + 82 q^{79} + 48 q^{80} + 162 q^{81} - 48 q^{82} + 1988 q^{83} - 60 q^{84} - 208 q^{85} + 928 q^{86} - 252 q^{87} + 352 q^{88} + 380 q^{89} + 950 q^{91} + 64 q^{92} - 126 q^{93} - 88 q^{94} + 572 q^{95} + 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.3.o.a 294.o 49.h $96$ $8.011$ None \(0\) \(24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{42}]$
294.3.o.b 294.o 49.h $120$ $8.011$ None \(0\) \(-30\) \(-12\) \(10\) $\mathrm{SU}(2)[C_{42}]$

Decomposition of \(S_{3}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)