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
Newforms 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: \(\Q(\zeta_{10})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into irreducible Hecke orbits

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

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