Properties

Label 693.2.cg
Level 693
Weight 2
Character orbit cg
Rep. character \(\chi_{693}(19,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 304
Newform subspaces 3
Sturm bound 192
Trace bound 4

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Defining parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 693.cg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(693, [\chi])\).

Total New Old
Modular forms 832 336 496
Cusp forms 704 304 400
Eisenstein series 128 32 96

Trace form

\( 304q + 5q^{2} - 41q^{4} + 3q^{5} - 5q^{7} + 40q^{8} + O(q^{10}) \) \( 304q + 5q^{2} - 41q^{4} + 3q^{5} - 5q^{7} + 40q^{8} + 3q^{11} - 4q^{14} + 13q^{16} + 45q^{17} - 15q^{19} + 52q^{22} + 14q^{23} - 31q^{25} - 51q^{26} + 20q^{28} - 27q^{31} + 75q^{35} + 7q^{37} - 9q^{38} - 105q^{40} + 52q^{44} - 20q^{46} + 21q^{47} + 23q^{49} - 30q^{50} - 15q^{52} - q^{53} + 112q^{56} - 6q^{58} - 45q^{59} - 30q^{61} - 132q^{64} - 36q^{67} - 105q^{68} + q^{70} + 12q^{71} - 60q^{73} - 85q^{74} - 30q^{79} - 153q^{80} + 63q^{82} - 190q^{85} - 84q^{86} - 21q^{88} - 6q^{89} - 20q^{91} + 174q^{92} - 15q^{94} - 40q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
693.2.cg.a \(48\) \(5.534\) None \(5\) \(0\) \(15\) \(-5\)
693.2.cg.b \(128\) \(5.534\) None \(0\) \(0\) \(0\) \(10\)
693.2.cg.c \(128\) \(5.534\) None \(0\) \(0\) \(-12\) \(-10\)

Decomposition of \(S_{2}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(693, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database