Properties

Label 261.3.s
Level $261$
Weight $3$
Character orbit 261.s
Rep. character $\chi_{261}(10,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $288$
Newform subspaces $3$
Sturm bound $90$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 3 \)
Sturm bound: \(90\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(261, [\chi])\).

Total New Old
Modular forms 768 312 456
Cusp forms 672 288 384
Eisenstein series 96 24 72

Trace form

\( 288q + 8q^{2} - 14q^{4} + 14q^{5} - 10q^{7} + 32q^{8} + O(q^{10}) \) \( 288q + 8q^{2} - 14q^{4} + 14q^{5} - 10q^{7} + 32q^{8} + 4q^{10} + 40q^{11} - 14q^{13} - 14q^{14} + 162q^{16} + 34q^{17} - 38q^{19} + 194q^{20} + 154q^{22} + 76q^{23} + 166q^{25} + 42q^{26} + 70q^{29} - 128q^{31} - 204q^{32} - 224q^{34} - 182q^{35} - 184q^{37} - 266q^{38} - 124q^{40} - 22q^{41} + 64q^{43} + 170q^{44} + 184q^{46} + 136q^{47} - 894q^{49} + 840q^{50} - 502q^{52} - 42q^{53} - 12q^{55} + 416q^{56} - 308q^{58} - 116q^{59} + 402q^{61} - 476q^{62} - 896q^{64} - 46q^{65} + 546q^{67} - 980q^{68} + 1302q^{70} - 1008q^{71} - 494q^{73} - 1440q^{74} - 678q^{76} - 900q^{77} - 252q^{79} - 1162q^{80} - 2q^{82} + 494q^{83} - 378q^{85} + 688q^{88} + 272q^{89} + 406q^{91} + 1022q^{92} - 1338q^{94} + 778q^{95} + 1268q^{97} + 1558q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(261, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
261.3.s.a \(48\) \(7.112\) None \(16\) \(0\) \(14\) \(-10\)
261.3.s.b \(120\) \(7.112\) None \(-8\) \(0\) \(0\) \(0\)
261.3.s.c \(120\) \(7.112\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(261, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(261, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)