Properties

Label 1925.2.b
Level $1925$
Weight $2$
Character orbit 1925.b
Rep. character $\chi_{1925}(1849,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $18$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1925.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(480\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1925, [\chi])\).

Total New Old
Modular forms 252 88 164
Cusp forms 228 88 140
Eisenstein series 24 0 24

Trace form

\( 88q - 100q^{4} + 16q^{6} - 76q^{9} + O(q^{10}) \) \( 88q - 100q^{4} + 16q^{6} - 76q^{9} - 8q^{11} + 8q^{14} + 124q^{16} - 32q^{19} + 8q^{24} - 24q^{26} + 40q^{29} + 20q^{31} - 40q^{34} + 68q^{36} - 16q^{39} - 16q^{41} + 20q^{44} + 80q^{46} - 88q^{49} + 24q^{51} + 40q^{54} - 24q^{56} - 44q^{59} - 196q^{64} - 36q^{69} - 44q^{71} + 208q^{76} - 24q^{79} + 8q^{81} - 40q^{86} + 108q^{89} - 16q^{91} - 16q^{94} - 80q^{96} + 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1925, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1925.2.b.a \(2\) \(15.371\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2q^{4}-iq^{7}+3q^{9}+q^{11}+\cdots\)
1925.2.b.b \(2\) \(15.371\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+iq^{7}+3iq^{8}+3q^{9}+\cdots\)
1925.2.b.c \(2\) \(15.371\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-iq^{7}+\cdots\)
1925.2.b.d \(2\) \(15.371\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-iq^{7}+\cdots\)
1925.2.b.e \(2\) \(15.371\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+2q^{4}-iq^{7}-6q^{9}-q^{11}+\cdots\)
1925.2.b.f \(2\) \(15.371\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+2q^{4}+iq^{7}-q^{9}-q^{11}+\cdots\)
1925.2.b.g \(2\) \(15.371\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2q^{4}+iq^{7}+2q^{9}-q^{11}+\cdots\)
1925.2.b.h \(4\) \(15.371\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-3q^{4}+(-5+\cdots)q^{6}+\cdots\)
1925.2.b.i \(4\) \(15.371\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1925.2.b.j \(4\) \(15.371\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1925.2.b.k \(4\) \(15.371\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1925.2.b.l \(4\) \(15.371\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1925.2.b.m \(6\) \(15.371\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1925.2.b.n \(6\) \(15.371\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1925.2.b.o \(6\) \(15.371\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1925.2.b.p \(8\) \(15.371\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{6})q^{2}-\beta _{7}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
1925.2.b.q \(14\) \(15.371\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2-\beta _{7}+\beta _{8}+\cdots)q^{4}+\cdots\)
1925.2.b.r \(14\) \(15.371\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-2+\beta _{2})q^{4}-\beta _{10}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1925, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)