Properties

Label 525.2.i
Level 525
Weight 2
Character orbit i
Rep. character \(\chi_{525}(151,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 50
Newforms 11
Sturm bound 160
Trace bound 2

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Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 525.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 11 \)
Sturm bound: \(160\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 184 50 134
Cusp forms 136 50 86
Eisenstein series 48 0 48

Trace form

\(50q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 26q^{4} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut -\mathstrut 25q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut 26q^{4} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut -\mathstrut 25q^{9} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 36q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut -\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 32q^{34} \) \(\mathstrut +\mathstrut 52q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut -\mathstrut 30q^{38} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 34q^{43} \) \(\mathstrut -\mathstrut 64q^{44} \) \(\mathstrut -\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 24q^{48} \) \(\mathstrut -\mathstrut 31q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 12q^{56} \) \(\mathstrut -\mathstrut 14q^{57} \) \(\mathstrut +\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 28q^{61} \) \(\mathstrut -\mathstrut 60q^{62} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 144q^{64} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 12q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 7q^{73} \) \(\mathstrut -\mathstrut 22q^{74} \) \(\mathstrut -\mathstrut 116q^{76} \) \(\mathstrut -\mathstrut 36q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 25q^{81} \) \(\mathstrut +\mathstrut 8q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut +\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 46q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 8q^{88} \) \(\mathstrut +\mathstrut 16q^{89} \) \(\mathstrut +\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 15q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut 16q^{96} \) \(\mathstrut +\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.i.a \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None \(-2\) \(1\) \(0\) \(1\) \(q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
525.2.i.b \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
525.2.i.c \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-5\) \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
525.2.i.d \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
525.2.i.e \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(0\) \(5\) \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
525.2.i.f \(4\) \(4.192\) \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
525.2.i.g \(4\) \(4.192\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(0\) \(2\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{3}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
525.2.i.h \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(4\) \(0\) \(2\) \(q+(-1-\beta _{1}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots\)
525.2.i.i \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(4\) \(0\) \(1\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
525.2.i.j \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-4\) \(0\) \(-1\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
525.2.i.k \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(-4\) \(0\) \(-2\) \(q+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)