Properties

Label 525.2.z
Level 525
Weight 2
Character orbit z
Rep. character \(\chi_{525}(64,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 128
Newform subspaces 2
Sturm bound 160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 525.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

Total New Old
Modular forms 336 128 208
Cusp forms 304 128 176
Eisenstein series 32 0 32

Trace form

\( 128q + 36q^{4} - 4q^{5} + 32q^{9} + O(q^{10}) \) \( 128q + 36q^{4} - 4q^{5} + 32q^{9} + 8q^{10} - 4q^{15} - 20q^{16} - 12q^{19} - 12q^{20} - 4q^{21} + 80q^{22} - 20q^{23} + 28q^{25} - 24q^{26} - 20q^{29} - 8q^{30} - 20q^{33} + 24q^{34} - 4q^{35} - 36q^{36} + 20q^{37} + 16q^{39} - 36q^{40} - 8q^{41} - 84q^{44} + 4q^{45} - 4q^{46} - 80q^{47} - 128q^{49} + 148q^{50} + 64q^{51} + 40q^{53} - 12q^{55} - 80q^{58} + 24q^{59} + 4q^{60} + 32q^{61} - 100q^{62} + 36q^{64} + 116q^{65} - 16q^{66} - 40q^{67} + 8q^{69} - 8q^{70} + 32q^{71} - 40q^{73} - 16q^{74} - 16q^{75} - 72q^{76} + 40q^{77} + 24q^{79} - 44q^{80} - 32q^{81} + 60q^{83} + 12q^{84} - 76q^{85} + 120q^{86} - 80q^{87} - 140q^{88} - 36q^{89} - 8q^{90} - 16q^{91} - 200q^{92} + 12q^{94} + 124q^{95} + 20q^{96} + 60q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
525.2.z.a \(56\) \(4.192\) None \(0\) \(0\) \(-2\) \(0\)
525.2.z.b \(72\) \(4.192\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database