Properties

Label 2450.2.c
Level $2450$
Weight $2$
Character orbit 2450.c
Rep. character $\chi_{2450}(99,\cdot)$
Character field $\Q$
Dimension $62$
Newform subspaces $24$
Sturm bound $840$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2450.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(840\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

Total New Old
Modular forms 468 62 406
Cusp forms 372 62 310
Eisenstein series 96 0 96

Trace form

\( 62q - 62q^{4} + 2q^{6} - 80q^{9} + O(q^{10}) \) \( 62q - 62q^{4} + 2q^{6} - 80q^{9} + 10q^{11} + 62q^{16} - 6q^{19} - 2q^{24} + 4q^{26} - 24q^{29} + 4q^{31} + 2q^{34} + 80q^{36} + 40q^{39} - 14q^{41} - 10q^{44} + 4q^{46} + 34q^{51} - 26q^{54} + 4q^{59} + 32q^{61} - 62q^{64} - 42q^{66} + 12q^{69} + 16q^{71} - 44q^{74} + 6q^{76} - 20q^{79} + 78q^{81} + 8q^{86} - 14q^{89} + 8q^{94} + 2q^{96} - 92q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2450.2.c.a \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{8}+\cdots\)
2450.2.c.b \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.c \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.d \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.e \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.f \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.g \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
2450.2.c.h \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
2450.2.c.i \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+3q^{9}-2q^{11}+\cdots\)
2450.2.c.j \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2q^{11}+\cdots\)
2450.2.c.k \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}+4q^{11}+\cdots\)
2450.2.c.l \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots\)
2450.2.c.m \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots\)
2450.2.c.n \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.o \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.p \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.q \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.r \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots\)
2450.2.c.s \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots\)
2450.2.c.t \(4\) \(19.563\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
2450.2.c.u \(4\) \(19.563\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{1}q^{8}+\cdots\)
2450.2.c.v \(4\) \(19.563\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
2450.2.c.w \(4\) \(19.563\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(2+\cdots)q^{6}+\cdots\)
2450.2.c.x \(8\) \(19.563\) 8.0.959512576.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{3}-\beta _{7})q^{3}-q^{4}+\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)