Properties

Label 2025.2.b
Level $2025$
Weight $2$
Character orbit 2025.b
Rep. character $\chi_{2025}(649,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $16$
Sturm bound $540$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(540\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2025, [\chi])\).

Total New Old
Modular forms 306 76 230
Cusp forms 234 68 166
Eisenstein series 72 8 64

Trace form

\( 68 q - 68 q^{4} + O(q^{10}) \) \( 68 q - 68 q^{4} + 68 q^{16} + 8 q^{19} + 16 q^{31} + 24 q^{34} - 48 q^{46} - 56 q^{61} - 32 q^{64} - 92 q^{76} - 4 q^{79} + 44 q^{91} - 60 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2025, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2025.2.b.a 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{4}-5q^{11}+2iq^{13}-4q^{16}+\cdots\)
2025.2.b.b 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{4}+5q^{11}-2iq^{13}-4q^{16}+\cdots\)
2025.2.b.c 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-3iq^{7}+3iq^{8}-2q^{11}+\cdots\)
2025.2.b.d 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{7}+3iq^{8}+2q^{11}+\cdots\)
2025.2.b.e 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{7}-3q^{11}-2iq^{13}+4q^{16}+\cdots\)
2025.2.b.f 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{7}+3q^{11}-2iq^{13}+4q^{16}+\cdots\)
2025.2.b.g 2025.b 5.b $4$ $16.170$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{2}+(-2+2\zeta_{12})q^{4}+(2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2025.2.b.h 2025.b 5.b $4$ $16.170$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{2}+(-2+2\zeta_{12})q^{4}+(-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2025.2.b.i 2025.b 5.b $4$ $16.170$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.j 2025.b 5.b $4$ $16.170$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.k 2025.b 5.b $4$ $16.170$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}-q^{4}-2\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
2025.2.b.l 2025.b 5.b $6$ $16.170$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{4}-\beta _{5})q^{7}+\cdots\)
2025.2.b.m 2025.b 5.b $6$ $16.170$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)
2025.2.b.n 2025.b 5.b $8$ $16.170$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{6})q^{4}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.o 2025.b 5.b $8$ $16.170$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.p 2025.b 5.b $8$ $16.170$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+\beta _{4}q^{4}+(-\beta _{1}+2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2025, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)