Properties

Label 100.4.c
Level $100$
Weight $4$
Character orbit 100.c
Rep. character $\chi_{100}(49,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $60$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(100, [\chi])\).

Total New Old
Modular forms 54 4 50
Cusp forms 36 4 32
Eisenstein series 18 0 18

Trace form

\( 4 q + 74 q^{9} + O(q^{10}) \) \( 4 q + 74 q^{9} - 30 q^{11} + 94 q^{19} - 76 q^{21} + 84 q^{29} + 404 q^{31} - 776 q^{39} - 546 q^{41} - 492 q^{49} + 378 q^{51} + 648 q^{59} - 352 q^{61} - 348 q^{69} + 552 q^{71} + 1252 q^{79} + 676 q^{81} + 1326 q^{89} - 464 q^{91} + 1020 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.4.c.a 100.c 5.b $2$ $5.900$ \(\Q(\sqrt{-1}) \) None 20.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+8iq^{7}+11q^{9}-60q^{11}+\cdots\)
100.4.c.b 100.c 5.b $2$ $5.900$ \(\Q(\sqrt{-1}) \) None 100.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-26iq^{7}+26q^{9}+45q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(100, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)