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Properties

Label 875.2.n
Level $875$
Weight $2$
Character orbit 875.n
Rep. character $\chi_{875}(99,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $184$
Newform subspaces $4$
Sturm bound $200$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 875 = 5^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 875.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(200\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(875, [\chi])\).

Total New Old
Modular forms 440 184 256
Cusp forms 360 184 176
Eisenstein series 80 0 80

Trace form

\( 184 q + 48 q^{4} + 54 q^{9} + O(q^{10}) \) \( 184 q + 48 q^{4} + 54 q^{9} - 8 q^{11} + 40 q^{12} + 4 q^{14} - 28 q^{16} - 12 q^{19} - 4 q^{21} + 30 q^{22} - 10 q^{23} + 28 q^{24} - 52 q^{26} - 30 q^{27} + 42 q^{29} - 12 q^{31} - 20 q^{33} - 60 q^{34} - 46 q^{36} + 70 q^{37} + 70 q^{38} + 4 q^{39} - 44 q^{41} - 50 q^{42} - 22 q^{44} + 4 q^{46} + 10 q^{47} - 30 q^{48} - 184 q^{49} + 44 q^{51} + 20 q^{53} - 54 q^{54} - 12 q^{56} - 10 q^{58} + 6 q^{59} - 36 q^{61} - 50 q^{62} - 20 q^{63} + 36 q^{64} + 74 q^{66} - 10 q^{67} - 42 q^{69} - 72 q^{71} - 140 q^{72} - 40 q^{73} - 20 q^{74} - 52 q^{76} + 20 q^{77} + 90 q^{78} - 68 q^{81} + 30 q^{83} + 12 q^{84} + 20 q^{86} - 30 q^{87} - 140 q^{88} - 18 q^{89} - 8 q^{91} - 80 q^{92} - 8 q^{94} - 52 q^{96} + 30 q^{97} + 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(875, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
875.2.n.a 875.n 25.e $8$ $6.987$ \(\Q(\zeta_{20})\) None 175.2.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\cdots\)
875.2.n.b 875.n 25.e $56$ $6.987$ None 175.2.h.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
875.2.n.c 875.n 25.e $56$ $6.987$ None 175.2.n.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
875.2.n.d 875.n 25.e $64$ $6.987$ None 175.2.h.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(875, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(875, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)