Properties

Label 3900.2.h
Level $3900$
Weight $2$
Character orbit 3900.h
Rep. character $\chi_{3900}(1249,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $12$
Sturm bound $1680$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3900.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1680\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3900, [\chi])\).

Total New Old
Modular forms 876 36 840
Cusp forms 804 36 768
Eisenstein series 72 0 72

Trace form

\( 36q - 36q^{9} + O(q^{10}) \) \( 36q - 36q^{9} - 8q^{11} - 8q^{19} + 8q^{21} - 8q^{29} + 24q^{31} + 16q^{41} - 60q^{49} + 8q^{51} - 48q^{59} - 16q^{61} - 8q^{69} + 16q^{71} + 40q^{79} + 36q^{81} + 56q^{89} + 16q^{91} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3900.2.h.a \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{7}-q^{9}-6q^{11}-iq^{13}+\cdots\)
3900.2.h.b \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2iq^{7}-q^{9}-4q^{11}+iq^{13}+\cdots\)
3900.2.h.c \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}-3q^{11}+iq^{13}+\cdots\)
3900.2.h.d \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots\)
3900.2.h.e \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2iq^{7}-q^{9}-iq^{13}-6iq^{17}+\cdots\)
3900.2.h.f \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{7}-q^{9}+q^{11}-iq^{13}+\cdots\)
3900.2.h.g \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{7}-q^{9}+q^{11}-iq^{13}+\cdots\)
3900.2.h.h \(2\) \(31.142\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}+3q^{11}+iq^{13}+\cdots\)
3900.2.h.i \(4\) \(31.142\) \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+(1-\beta _{3})q^{11}+\cdots\)
3900.2.h.j \(4\) \(31.142\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+(2-\beta _{3})q^{11}+\cdots\)
3900.2.h.k \(6\) \(31.142\) 6.0.60217600.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{5})q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
3900.2.h.l \(6\) \(31.142\) 6.0.146700544.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+(2-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1950, [\chi])\)\(^{\oplus 2}\)