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Properties

Label 354.2.e
Level $354$
Weight $2$
Character orbit 354.e
Rep. character $\chi_{354}(7,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $280$
Newform subspaces $4$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 354.e (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(354, [\chi])\).

Total New Old
Modular forms 1792 280 1512
Cusp forms 1568 280 1288
Eisenstein series 224 0 224

Trace form

\( 280 q - 10 q^{4} + 2 q^{6} + 4 q^{7} - 10 q^{9} + O(q^{10}) \) \( 280 q - 10 q^{4} + 2 q^{6} + 4 q^{7} - 10 q^{9} + 8 q^{10} + 16 q^{11} + 12 q^{13} + 16 q^{14} + 4 q^{15} - 10 q^{16} + 24 q^{17} + 16 q^{19} + 12 q^{22} + 32 q^{23} + 2 q^{24} + 10 q^{25} + 8 q^{26} + 4 q^{28} + 48 q^{29} + 4 q^{30} + 36 q^{31} + 8 q^{33} + 24 q^{34} + 56 q^{35} - 10 q^{36} + 20 q^{37} + 32 q^{38} + 8 q^{39} + 8 q^{40} + 40 q^{41} + 16 q^{42} + 44 q^{43} + 16 q^{44} - 84 q^{46} - 84 q^{47} - 166 q^{49} - 216 q^{50} + 24 q^{51} - 104 q^{52} - 152 q^{53} + 2 q^{54} - 276 q^{55} + 16 q^{56} + 16 q^{57} - 92 q^{58} - 172 q^{59} + 4 q^{60} - 164 q^{61} - 68 q^{62} + 4 q^{63} - 10 q^{64} - 228 q^{65} + 8 q^{66} - 132 q^{67} - 92 q^{68} + 40 q^{69} - 160 q^{70} - 120 q^{71} - 68 q^{74} + 32 q^{75} + 16 q^{76} + 128 q^{77} + 24 q^{78} + 108 q^{79} - 10 q^{81} + 32 q^{82} + 104 q^{83} + 120 q^{85} + 64 q^{86} + 36 q^{87} + 12 q^{88} + 64 q^{89} + 8 q^{90} + 112 q^{91} + 32 q^{92} + 20 q^{93} + 56 q^{94} + 104 q^{95} + 2 q^{96} + 108 q^{97} + 64 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
354.2.e.a 354.e 59.c $56$ $2.827$ None \(-2\) \(-2\) \(4\) \(9\) $\mathrm{SU}(2)[C_{29}]$
354.2.e.b 354.e 59.c $56$ $2.827$ None \(2\) \(2\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{29}]$
354.2.e.c 354.e 59.c $84$ $2.827$ None \(-3\) \(3\) \(0\) \(1\) $\mathrm{SU}(2)[C_{29}]$
354.2.e.d 354.e 59.c $84$ $2.827$ None \(3\) \(-3\) \(-2\) \(-7\) $\mathrm{SU}(2)[C_{29}]$

Decomposition of \(S_{2}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(118, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)