Properties

Label 100.2.c
Level $100$
Weight $2$
Character orbit 100.c
Rep. character $\chi_{100}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 100.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(100, [\chi])\).

Total New Old
Modular forms 24 2 22
Cusp forms 6 2 4
Eisenstein series 18 0 18

Trace form

\( 2q - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{9} + 8q^{19} - 8q^{21} - 12q^{29} - 8q^{31} + 8q^{39} + 12q^{41} + 6q^{49} + 24q^{51} - 24q^{59} + 4q^{61} + 24q^{69} - 24q^{71} - 16q^{79} - 22q^{81} + 12q^{89} + 8q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
100.2.c.a \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}-iq^{13}-3iq^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)