Properties

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

Related objects

Downloads

Learn more about

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: \(\Q(\zeta_{29})\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(354, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
354.2.e.a \(56\) \(2.827\) None \(-2\) \(-2\) \(4\) \(9\)
354.2.e.b \(56\) \(2.827\) None \(2\) \(2\) \(-2\) \(1\)
354.2.e.c \(84\) \(2.827\) None \(-3\) \(3\) \(0\) \(1\)
354.2.e.d \(84\) \(2.827\) None \(3\) \(-3\) \(-2\) \(-7\)

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

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