Properties

Label 525.2.j
Level 525
Weight 2
Character orbit j
Rep. character \(\chi_{525}(218,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 72
Newform subspaces 3
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
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 184 72 112
Cusp forms 136 72 64
Eisenstein series 48 0 48

Trace form

\( 72q + 4q^{3} + O(q^{10}) \) \( 72q + 4q^{3} - 16q^{12} + 8q^{13} - 88q^{16} + 20q^{18} - 8q^{21} - 8q^{22} + 16q^{27} - 28q^{33} - 32q^{36} + 16q^{37} + 20q^{42} + 40q^{43} + 128q^{46} - 16q^{48} - 80q^{51} - 4q^{57} - 40q^{58} - 64q^{61} + 8q^{63} + 152q^{66} - 24q^{67} + 8q^{72} - 32q^{73} - 64q^{76} - 60q^{78} + 16q^{81} + 80q^{82} - 4q^{87} - 96q^{88} + 48q^{91} + 76q^{93} + 192q^{96} - 24q^{97} + O(q^{100}) \)

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.j.a \(16\) \(4.192\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{10}+\beta _{13}-\beta _{15})q^{2}+\beta _{7}q^{3}+\cdots\)
525.2.j.b \(24\) \(4.192\) None \(0\) \(4\) \(0\) \(0\)
525.2.j.c \(32\) \(4.192\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T^{4} + 24 T^{8} + 16 T^{12} + 256 T^{16} )^{2} \))
$3$ (\( 1 - 7 T^{4} - 32 T^{8} - 567 T^{12} + 6561 T^{16} \))
$5$ 1
$7$ (\( ( 1 + T^{4} )^{4} \))
$11$ (\( ( 1 + 7 T^{2} + 180 T^{4} + 847 T^{6} + 14641 T^{8} )^{4} \))
$13$ (\( ( 1 - 47 T^{4} + 47568 T^{8} - 1342367 T^{12} + 815730721 T^{16} )^{2} \))
$17$ (\( ( 1 + 193 T^{4} - 1920 T^{8} + 16119553 T^{12} + 6975757441 T^{16} )^{2} \))
$19$ (\( ( 1 - 22 T^{2} + 361 T^{4} )^{8} \))
$23$ (\( ( 1 + 98 T^{4} + 279841 T^{8} )^{4} \))
$29$ (\( ( 1 + 73 T^{2} + 2808 T^{4} + 61393 T^{6} + 707281 T^{8} )^{4} \))
$31$ (\( ( 1 + 2 T + 30 T^{2} + 62 T^{3} + 961 T^{4} )^{8} \))
$37$ (\( ( 1 - 2012 T^{4} + 3915558 T^{8} - 3770811932 T^{12} + 3512479453921 T^{16} )^{2} \))
$41$ (\( ( 1 + 8 T^{2} + 78 T^{4} + 13448 T^{6} + 2825761 T^{8} )^{4} \))
$43$ (\( ( 1 - 3214 T^{4} + 3418801 T^{8} )^{4} \))
$47$ (\( ( 1 - 2087 T^{4} + 6045360 T^{8} - 10183894247 T^{12} + 23811286661761 T^{16} )^{2} \))
$53$ (\( ( 1 - 3836 T^{4} + 14179686 T^{8} - 30267885116 T^{12} + 62259690411361 T^{16} )^{2} \))
$59$ (\( ( 1 + 64 T^{2} + 4686 T^{4} + 222784 T^{6} + 12117361 T^{8} )^{4} \))
$61$ (\( ( 1 - 2 T + 90 T^{2} - 122 T^{3} + 3721 T^{4} )^{8} \))
$67$ (\( ( 1 + 388 T^{4} - 29618010 T^{8} + 7818634948 T^{12} + 406067677556641 T^{16} )^{2} \))
$71$ (\( ( 1 - 208 T^{2} + 19710 T^{4} - 1048528 T^{6} + 25411681 T^{8} )^{4} \))
$73$ (\( ( 1 - 188 T^{4} - 49166394 T^{8} - 5338869308 T^{12} + 806460091894081 T^{16} )^{2} \))
$79$ (\( ( 1 - 83 T^{2} + 1656 T^{4} - 518003 T^{6} + 38950081 T^{8} )^{4} \))
$83$ (\( ( 1 - 9692 T^{4} + 102045030 T^{8} - 459966047132 T^{12} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( ( 1 + 52 T^{2} - 2490 T^{4} + 411892 T^{6} + 62742241 T^{8} )^{4} \))
$97$ (\( ( 1 + 31201 T^{4} + 419298624 T^{8} + 2762202096481 T^{12} + 7837433594376961 T^{16} )^{2} \))
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