Properties

Label 5780.2.c
Level $5780$
Weight $2$
Character orbit 5780.c
Rep. character $\chi_{5780}(5201,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $10$
Sturm bound $1836$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 5780 = 2^{2} \cdot 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5780.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(1836\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5780, [\chi])\).

Total New Old
Modular forms 972 90 882
Cusp forms 864 90 774
Eisenstein series 108 0 108

Trace form

\( 90q - 82q^{9} + O(q^{10}) \) \( 90q - 82q^{9} - 4q^{15} - 16q^{19} + 32q^{21} - 90q^{25} + 20q^{33} + 8q^{35} + 16q^{43} - 36q^{47} - 94q^{49} - 48q^{53} - 16q^{55} + 12q^{59} + 4q^{67} - 24q^{69} - 24q^{77} + 58q^{81} - 8q^{83} + 72q^{87} + 36q^{89} + 52q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5780, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5780.2.c.a \(2\) \(46.154\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+iq^{5}+2iq^{7}-q^{9}+2q^{13}+\cdots\)
5780.2.c.b \(2\) \(46.154\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}-iq^{5}-2iq^{7}-q^{9}-5iq^{11}+\cdots\)
5780.2.c.c \(2\) \(46.154\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+4iq^{7}+3q^{9}-2iq^{11}-6q^{13}+\cdots\)
5780.2.c.d \(2\) \(46.154\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}-2iq^{7}+3q^{9}+iq^{11}-3q^{19}+\cdots\)
5780.2.c.e \(4\) \(46.154\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
5780.2.c.f \(6\) \(46.154\) 6.0.2611456.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(-2+\beta _{1}+\cdots)q^{9}+\cdots\)
5780.2.c.g \(12\) \(46.154\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{3}-\beta _{3}q^{5}-\beta _{6}q^{7}+\beta _{8}q^{9}+\cdots\)
5780.2.c.h \(12\) \(46.154\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}-\beta _{6}q^{5}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\)
5780.2.c.i \(24\) \(46.154\) None \(0\) \(0\) \(0\) \(0\)
5780.2.c.j \(24\) \(46.154\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(5780, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5780, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1445, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2890, [\chi])\)\(^{\oplus 2}\)