Properties

Label 1725.2.b
Level $1725$
Weight $2$
Character orbit 1725.b
Rep. character $\chi_{1725}(1174,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $21$
Sturm bound $480$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1725.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(480\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1725, [\chi])\).

Total New Old
Modular forms 252 64 188
Cusp forms 228 64 164
Eisenstein series 24 0 24

Trace form

\( 64q - 60q^{4} - 4q^{6} - 64q^{9} + O(q^{10}) \) \( 64q - 60q^{4} - 4q^{6} - 64q^{9} - 8q^{14} + 68q^{16} + 4q^{19} - 4q^{21} + 12q^{24} + 8q^{26} + 24q^{29} - 28q^{31} - 8q^{34} + 60q^{36} + 20q^{39} - 64q^{41} + 24q^{44} - 8q^{46} - 28q^{49} + 4q^{54} + 48q^{56} - 48q^{59} - 52q^{61} - 44q^{64} + 32q^{66} + 8q^{69} + 56q^{71} + 112q^{74} + 8q^{76} - 8q^{79} + 64q^{81} - 32q^{84} + 96q^{86} + 72q^{89} + 20q^{91} + 40q^{94} - 28q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1725, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1725.2.b.a \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+5iq^{7}+\cdots\)
1725.2.b.b \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+3iq^{7}+\cdots\)
1725.2.b.c \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots\)
1725.2.b.d \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+5iq^{7}+\cdots\)
1725.2.b.e \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{7}+\cdots\)
1725.2.b.f \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+4iq^{7}+\cdots\)
1725.2.b.g \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}-2iq^{7}+\cdots\)
1725.2.b.h \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}-3iq^{7}+\cdots\)
1725.2.b.i \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-6q^{11}+\cdots\)
1725.2.b.j \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2q^{4}+3iq^{7}-q^{9}-4q^{11}+\cdots\)
1725.2.b.k \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2q^{4}-3iq^{7}-q^{9}+2q^{11}+\cdots\)
1725.2.b.l \(2\) \(13.774\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2q^{4}-iq^{7}-q^{9}+4q^{11}+\cdots\)
1725.2.b.m \(4\) \(13.774\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}-4q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots\)
1725.2.b.n \(4\) \(13.774\) \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1725.2.b.o \(4\) \(13.774\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1725.2.b.p \(4\) \(13.774\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+(-2+\cdots)q^{4}+\cdots\)
1725.2.b.q \(4\) \(13.774\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
1725.2.b.r \(4\) \(13.774\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
1725.2.b.s \(4\) \(13.774\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1725.2.b.t \(6\) \(13.774\) 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{4}+\cdots)q^{4}+\cdots\)
1725.2.b.u \(6\) \(13.774\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{2}q^{3}+(-1-\beta _{1})q^{4}+\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1725, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1725, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)