Properties

Label 900.3.c
Level $900$
Weight $3$
Character orbit 900.c
Rep. character $\chi_{900}(451,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $21$
Sturm bound $540$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(540\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 384 98 286
Cusp forms 336 92 244
Eisenstein series 48 6 42

Trace form

\( 92q + 2q^{4} - 12q^{8} + O(q^{10}) \) \( 92q + 2q^{4} - 12q^{8} - 24q^{14} - 22q^{16} - 4q^{17} - 8q^{22} - 44q^{26} + 56q^{28} - 20q^{29} + 20q^{32} - 6q^{34} - 88q^{37} + 112q^{38} + 4q^{41} - 90q^{44} + 84q^{46} - 556q^{49} - 72q^{52} + 28q^{53} + 420q^{56} - 56q^{58} + 48q^{61} - 112q^{62} - 118q^{64} - 360q^{68} + 88q^{73} - 92q^{74} - 78q^{76} + 48q^{77} + 72q^{82} - 276q^{86} + 352q^{88} + 220q^{89} + 216q^{92} - 120q^{94} - 152q^{97} + 760q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
900.3.c.a \(1\) \(24.523\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+4q^{4}-8q^{8}-24q^{13}+2^{4}q^{16}+\cdots\)
900.3.c.b \(1\) \(24.523\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+4q^{4}-8q^{8}+10q^{13}+2^{4}q^{16}+\cdots\)
900.3.c.c \(1\) \(24.523\) \(\Q\) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(0\) \(0\) \(q+2q^{2}+4q^{4}+8q^{8}+10q^{13}+2^{4}q^{16}+\cdots\)
900.3.c.d \(1\) \(24.523\) \(\Q\) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(0\) \(0\) \(q+2q^{2}+4q^{4}+8q^{8}+24q^{13}+2^{4}q^{16}+\cdots\)
900.3.c.e \(2\) \(24.523\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-2-2\zeta_{6})q^{4}-4\zeta_{6}q^{7}+\cdots\)
900.3.c.f \(2\) \(24.523\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}-6\zeta_{6}q^{7}+\cdots\)
900.3.c.g \(2\) \(24.523\) \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{-15}) \) \(-1\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+(-4+\beta )q^{4}+(4+3\beta )q^{8}+\cdots\)
900.3.c.h \(2\) \(24.523\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-4q^{4}+2iq^{7}+4iq^{8}+8q^{14}+\cdots\)
900.3.c.i \(2\) \(24.523\) \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{-15}) \) \(1\) \(0\) \(0\) \(0\) \(q+(1-\beta )q^{2}+(-3-\beta )q^{4}+(-7+3\beta )q^{8}+\cdots\)
900.3.c.j \(2\) \(24.523\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{2}+(-2-2\zeta_{6})q^{4}-6\zeta_{6}q^{7}+\cdots\)
900.3.c.k \(4\) \(24.523\) \(\Q(\zeta_{10})\) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{10}q^{2}+(-1+\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots\)
900.3.c.l \(4\) \(24.523\) 4.0.8405.1 None \(-1\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{4}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
900.3.c.m \(4\) \(24.523\) 4.0.8405.1 None \(1\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
900.3.c.n \(8\) \(24.523\) 8.0.4069419264.1 None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-1+\beta _{7})q^{4}+(-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
900.3.c.o \(8\) \(24.523\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{3}-\beta _{7})q^{7}+\cdots\)
900.3.c.p \(8\) \(24.523\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(1+\beta _{7})q^{4}-\beta _{2}q^{7}+(-\beta _{5}+\cdots)q^{8}+\cdots\)
900.3.c.q \(8\) \(24.523\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{4}q^{7}-\beta _{3}q^{8}+\cdots\)
900.3.c.r \(8\) \(24.523\) 8.0.6080256576.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(1+\beta _{7})q^{4}+(\beta _{2}+\beta _{4})q^{7}+\cdots\)
900.3.c.s \(8\) \(24.523\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{5})q^{4}-\beta _{3}q^{7}+\cdots\)
900.3.c.t \(8\) \(24.523\) 8.0.4069419264.1 None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{5})q^{4}+\cdots\)
900.3.c.u \(8\) \(24.523\) 8.0.85100625.1 None \(4\) \(0\) \(0\) \(0\) \(q+(1-\beta _{5})q^{2}+(1-\beta _{4})q^{4}+(-1-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)