Properties

Label 4100.2.d
Level $4100$
Weight $2$
Character orbit 4100.d
Rep. character $\chi_{4100}(1149,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $7$
Sturm bound $1260$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4100 = 2^{2} \cdot 5^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4100.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(1260\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4100, [\chi])\).

Total New Old
Modular forms 648 60 588
Cusp forms 612 60 552
Eisenstein series 36 0 36

Trace form

\( 60q - 56q^{9} + O(q^{10}) \) \( 60q - 56q^{9} - 8q^{11} - 4q^{21} + 20q^{29} + 24q^{31} - 12q^{39} - 8q^{41} - 76q^{49} + 4q^{51} + 8q^{59} + 16q^{61} - 28q^{69} + 60q^{71} + 40q^{79} + 108q^{81} - 20q^{91} + 20q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4100, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4100.2.d.a \(4\) \(32.739\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots\)
4100.2.d.b \(4\) \(32.739\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(\beta _{1}+\beta _{3})q^{7}+2q^{9}+(3+4\beta _{2}+\cdots)q^{11}+\cdots\)
4100.2.d.c \(8\) \(32.739\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{4}+\beta _{6})q^{3}+(\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots\)
4100.2.d.d \(8\) \(32.739\) 8.0.4569760000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)
4100.2.d.e \(8\) \(32.739\) 8.0.2732361984.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{5}q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4100.2.d.f \(14\) \(32.739\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{11}q^{7}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
4100.2.d.g \(14\) \(32.739\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(\beta _{2}+\beta _{3})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(820, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1025, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2050, [\chi])\)\(^{\oplus 2}\)