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Properties

Label 525.2.bc
Level $525$
Weight $2$
Character orbit 525.bc
Rep. character $\chi_{525}(82,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $96$
Newform subspaces $5$
Sturm bound $160$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(160\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 368 96 272
Cusp forms 272 96 176
Eisenstein series 96 0 96

Trace form

\( 96 q - 8 q^{7} + 24 q^{8} + O(q^{10}) \) \( 96 q - 8 q^{7} + 24 q^{8} + 16 q^{11} + 80 q^{16} - 4 q^{21} + 8 q^{22} + 8 q^{23} - 48 q^{26} + 24 q^{28} - 48 q^{31} - 24 q^{32} + 36 q^{33} - 96 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} + 16 q^{51} + 108 q^{52} + 24 q^{53} + 96 q^{56} - 16 q^{57} - 4 q^{58} - 12 q^{61} - 4 q^{63} - 144 q^{66} - 8 q^{67} - 132 q^{68} + 32 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 48 q^{81} - 12 q^{82} - 88 q^{86} + 24 q^{87} + 32 q^{88} - 92 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.2.bc.a 525.bc 35.k $8$ $4.192$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{3}+(-2\zeta_{24}^{2}+2\zeta_{24}^{6})q^{4}+\cdots\)
525.2.bc.b 525.bc 35.k $8$ $4.192$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(2\zeta_{24}-\zeta_{24}^{5})q^{2}+\zeta_{24}^{7}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
525.2.bc.c 525.bc 35.k $24$ $4.192$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
525.2.bc.d 525.bc 35.k $24$ $4.192$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
525.2.bc.e 525.bc 35.k $32$ $4.192$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$

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

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