Properties

Label 2475.2.c
Level $2475$
Weight $2$
Character orbit 2475.c
Rep. character $\chi_{2475}(199,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $20$
Sturm bound $720$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(720\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 384 76 308
Cusp forms 336 76 260
Eisenstein series 48 0 48

Trace form

\( 76q - 86q^{4} + O(q^{10}) \) \( 76q - 86q^{4} - 4q^{11} - 4q^{14} + 98q^{16} - 12q^{19} - 8q^{26} - 40q^{29} + 22q^{31} + 28q^{34} + 40q^{41} + 18q^{44} - 72q^{46} - 48q^{49} + 36q^{56} + 26q^{59} + 12q^{61} - 94q^{64} - 98q^{71} + 48q^{74} - 12q^{76} + 32q^{79} - 16q^{86} - 50q^{89} - 76q^{91} + 112q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2475.2.c.a \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2q^{4}-2iq^{7}-q^{11}-4iq^{13}+\cdots\)
2475.2.c.b \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}-q^{11}+\cdots\)
2475.2.c.c \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}-3iq^{7}+3iq^{8}-q^{11}+\cdots\)
2475.2.c.d \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}-4iq^{7}+3iq^{8}-q^{11}+\cdots\)
2475.2.c.e \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+3iq^{7}+3iq^{8}+q^{11}+\cdots\)
2475.2.c.f \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+3iq^{8}+q^{11}+2iq^{13}+\cdots\)
2475.2.c.g \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}-2iq^{7}+3iq^{8}+q^{11}+\cdots\)
2475.2.c.h \(2\) \(19.763\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+iq^{7}+q^{11}-iq^{13}+4q^{16}+\cdots\)
2475.2.c.i \(4\) \(19.763\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
2475.2.c.j \(4\) \(19.763\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
2475.2.c.k \(4\) \(19.763\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2475.2.c.l \(4\) \(19.763\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
2475.2.c.m \(4\) \(19.763\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}-2\zeta_{8}^{2}q^{7}+\cdots\)
2475.2.c.n \(4\) \(19.763\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}-q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
2475.2.c.o \(4\) \(19.763\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
2475.2.c.p \(4\) \(19.763\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots\)
2475.2.c.q \(6\) \(19.763\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{4})q^{2}+(-3-\beta _{1})q^{4}+(\beta _{3}+\cdots)q^{7}+\cdots\)
2475.2.c.r \(6\) \(19.763\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
2475.2.c.s \(8\) \(19.763\) 8.0.9488318464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
2475.2.c.t \(8\) \(19.763\) 8.0.9488318464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)